# How do you solve 4x^2-14x-8=0?

Jul 8, 2015

The solutions for the equation are
color(blue)(x=4, x=-1/2

#### Explanation:

$4 {x}^{2} - 14 x - 8 = 0$

We can first factorise the equation and then find the solutions :

Factorising by splitting the middle term:

$4 {x}^{2} - 14 x - 8 = 0$

$4 {x}^{2} + \textcolor{b l u e}{2 x - 16 x} - 2 = 0$

$2 x \left(2 x + 1\right) - 8 \left(2 x + 1\right) = 0$

color(blue)((2x -8)(2x+1) = 0

Now, equating the factors with zero to obtain the solutions
2x -8 = 0 , color(blue)(x=8/2 = 4
2x+1 = 0 ,color(blue)( x =-1/2