What are the solutions to the equation -1/3 x^2-10x+112= 1/4 x^2+5x+1 ?

The solutions to the equation -1/3 x^2-10x+112= 1/4 x^2+5x+1 are x=-222/7 ,x=6

Find the zeros of -1/3 x^2-10x+112= 1/4 x^2+5x+1

The zeros of -1/3 x^2-10x+112= 1/4 x^2+5x+1 are x=-222/7 ,x=6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

- \frac{1}{3} x^{2} - 10 x + 112 = \frac{1}{4} x^{2} + 5 x + 1

x = - \frac{222}{7}, x = 6

Decimal Notation

x = - 31.71428 \dots, x = 6

Solution steps

- \frac{1}{3} x^{2} - 10 x + 112 = \frac{1}{4} x^{2} + 5 x + 1

Find Least Common Multiplier of

3, 4 : 12

Multiply by LCM=

12

- \frac{1}{3} x^{2} \cdot 12 - 10 x \cdot 12 + 112 \cdot 12 = \frac{1}{4} x^{2} \cdot 12 + 5 x \cdot 12 + 1 \cdot 12

Simplify

- 4 x^{2} - 120 x + 1344 = 3 x^{2} + 60 x + 12

Move

12

to the left side

- 4 x^{2} - 120 x + 1332 = 3 x^{2} + 60 x

Move

60 x

to the left side

- 4 x^{2} - 180 x + 1332 = 3 x^{2}

Move

3 x^{2}

to the left side

- 7 x^{2} - 180 x + 1332 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 180 ) \pm ( - 180 ) ^{2} - 4 ( - 7 ) \cdot 1332}{2 ( - 7 )}

(- 180)^{2} - 4 (- 7) \cdot 1332 = 264

x_{1, 2} = \frac{- ( - 180 ) \pm 264}{2 ( - 7 )}

Separate the solutions

x_{1} = \frac{- ( - 180 ) + 264}{2 ( - 7 )}, x_{2} = \frac{- ( - 180 ) - 264}{2 ( - 7 )}

x = \frac{- ( - 180 ) + 264}{2 ( - 7 )} : - \frac{222}{7}

x = \frac{- ( - 180 ) - 264}{2 ( - 7 )} : 6

The solutions to the quadratic equation are:

x = - \frac{222}{7}, x = 6

x, x^{2} + y^{2} + z^{2} = 2 y

(4 - 4 x + x^{2}) (6 \cdot 1 0^{- 6}) = x^{2} (15 \cdot 1 0^{- 6})

(s - 5) (s + 3) = 0

2 x^{2} - 4 x + 16 = 0

x^{2} - 2 x - 15 = - x + 5

What are the solutions to the equation -1/3 x^2-10x+112= 1/4 x^2+5x+1 ?
The solutions to the equation -1/3 x^2-10x+112= 1/4 x^2+5x+1 are x=-222/7 ,x=6
Find the zeros of -1/3 x^2-10x+112= 1/4 x^2+5x+1
The zeros of -1/3 x^2-10x+112= 1/4 x^2+5x+1 are x=-222/7 ,x=6