en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(3x+1)/3-(2x^2-5)/6 =(7x+4)/2

Solution

\frac{3 x + 1}{3} - \frac{2 x ^{2} - 5}{6} = \frac{7 x + 4}{2}

Solution

x = - \frac{15 + 185}{4}, x = - \frac{15 - 185}{4}

+1

Decimal Notation

x = - 7.15036 \dots, x = - 0.34963 \dots

Solution steps

\frac{3 x + 1}{3} - \frac{2 x ^{2} - 5}{6} = \frac{7 x + 4}{2}

Find Least Common Multiplier of

3, 6, 2 : 6

Multiply by LCM=

6

\frac{3 x + 1}{3} \cdot 6 - \frac{2 x ^{2} - 5}{6} \cdot 6 = \frac{7 x + 4}{2} \cdot 6

Simplify

2 (3 x + 1) - (2 x^{2} - 5) = 3 (7 x + 4)

Expand

2 (3 x + 1) - (2 x^{2} - 5) : - 2 x^{2} + 6 x + 7

Expand

3 (7 x + 4) : 21 x + 12

- 2 x^{2} + 6 x + 7 = 21 x + 12

Move

12

to the left side

- 2 x^{2} + 6 x - 5 = 21 x

Move

21 x

to the left side

- 2 x^{2} - 15 x - 5 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 15 ) \pm ( - 15 ) ^{2} - 4 ( - 2 ) ( - 5 )}{2 ( - 2 )}

(- 15)^{2} - 4 (- 2) (- 5) = 185

x_{1, 2} = \frac{- ( - 15 ) \pm 185}{2 ( - 2 )}

Separate the solutions

x_{1} = \frac{- ( - 15 ) + 185}{2 ( - 2 )}, x_{2} = \frac{- ( - 15 ) - 185}{2 ( - 2 )}

x = \frac{- ( - 15 ) + 185}{2 ( - 2 )} : - \frac{15 + 185}{4}

x = \frac{- ( - 15 ) - 185}{2 ( - 2 )} : - \frac{15 - 185}{4}

The solutions to the quadratic equation are:

x = - \frac{15 + 185}{4}, x = - \frac{15 - 185}{4}

Popular Examples

x^{2} - 56 = 0

x^{2} + 1.32 = - 1.4 x

solvefor b,Db^2-4g=m solve for

b, D b^{2} - 4 g = m

x^{2} + 13 x + 39 = 0

1+4+7+(3n-2)=(n(3n-1))/2 ,n>= 1

1 + 4 + 7 + (3 n - 2) = \frac{n ( 3 n - 1 )}{2}, n \geq 1