What are the solutions to the equation 5(m+n-1)x^2+4(m-n)x+(mn)/(12)=0 ?

The solutions to the equation 5(m+n-1)x^2+4(m-n)x+(mn)/(12)=0 are

Find the zeros of 5(m+n-1)x^2+4(m-n)x+(mn)/(12)=0

The zeros of 5(m+n-1)x^2+4(m-n)x+(mn)/(12)=0 are

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

5 (m + n - 1) x^{2} + 4 (m - n) x + \frac{mn}{12} = 0

x = \frac{- 48 m + 48 n + - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}, x = \frac{- 48 m + 48 n - - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}; 60 m + 60 n - 60 \neq = 0

Solution steps

5 (m + n - 1) x^{2} + 4 (m - n) x + \frac{mn}{12} = 0

Multiply both sides by

12

60 x^{2} (m + n - 1) + 48 x (m - n) + mn = 0

Expand

60 x^{2} (m + n - 1) + 48 x (m - n) + mn : 60 m x^{2} + 60 n x^{2} - 60 x^{2} + 48 m x - 48 n x + mn

60 m x^{2} + 60 n x^{2} - 60 x^{2} + 48 m x - 48 n x + mn = 0

Write in the standard form

a x^{2} + b x + c = 0

(60 m + 60 n - 60) x^{2} + (48 m - 48 n) x + mn = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( 48 m - 48 n ) \pm ( 48 m - 48 n ) ^{2} - 4 ( 60 m + 60 n - 60 ) mn}{2 ( 60 m + 60 n - 60 )}

Simplify

(48 m - 48 n)^{2} - 4 (60 m + 60 n - 60) mn : - 240 m^{2} n + 2304 m^{2} - 240 m n^{2} - 4368 mn + 2304 n^{2}

x_{1, 2} = \frac{- ( 48 m - 48 n ) \pm - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}; 60 m + 60 n - 60 \neq = 0

Separate the solutions

x_{1} = \frac{- ( 48 m - 48 n ) + - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}, x_{2} = \frac{- ( 48 m - 48 n ) - - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}

x = \frac{- ( 48 m - 48 n ) + - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )} : \frac{- 48 m + 48 n + - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}

x = \frac{- ( 48 m - 48 n ) - - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )} : \frac{- 48 m + 48 n - - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}

The solutions to the quadratic equation are:

x = \frac{- 48 m + 48 n + - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}, x = \frac{- 48 m + 48 n - - 240 m ^{2} n + 2304 m ^{2} - 240 m n ^{2} - 4368 mn + 2304 n ^{2}}{2 ( 60 m + 60 n - 60 )}; 60 m + 60 n - 60 \neq = 0

x^{2} - 7 x - 144 = 0

9 w^{2} - 27 w + 20 = 0

16 x^{2} - 25 x = - 9

- x^{2} + 2 x = 2

8 x^{2} + 7 = 5 x^{2} + 4

What are the solutions to the equation 5(m+n-1)x^2+4(m-n)x+(mn)/(12)=0 ?
The solutions to the equation 5(m+n-1)x^2+4(m-n)x+(mn)/(12)=0 are
Find the zeros of 5(m+n-1)x^2+4(m-n)x+(mn)/(12)=0
The zeros of 5(m+n-1)x^2+4(m-n)x+(mn)/(12)=0 are