# How do you solve 2x^2 -: 3x = 14 ?

Aug 20, 2016

See explanation...

#### Explanation:

I think the question should have had subtraction rather than division, but I will answer both possibilities:

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How to solve $\boldsymbol{\frac{2 {x}^{2}}{3 x} = 14}$

Multiply both sides by $3 x$ to get:

$2 {x}^{2} = 42 x$

Divide both sides by $2 x$ to find:

$x = 21$

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How to solve $\boldsymbol{2 {x}^{2} - 3 x = 14}$

Subtract $14$ from both sides to get:

$2 {x}^{2} - 3 x - 14 = 0$

Use an AC method to factorise:

Look for a pair of factors of $A C = 2 \cdot 14 = 28$ which differ by $B = 3$.

The pair $7 , 4$ works.

Use this to split the middle term then factor by grouping:

$0 = 2 {x}^{2} - 3 x - 14$

$= 2 {x}^{2} - 7 x + 4 x - 14$

$= \left(2 {x}^{2} - 7 x\right) + \left(4 x - 14\right)$

$= x \left(2 x - 7\right) + 2 \left(2 x - 7\right)$

$= \left(x + 2\right) \left(2 x - 7\right)$

Hence $x = - 2$ or $x = \frac{7}{2}$