4x^2-9x-8=-4x

Solution for 4x^2-9x-8=-4x equation:

4x^2-9x-8=-4x

We move all terms to the left:

4x^2-9x-8-(-4x)=0

We get rid of parentheses

4x^2-9x+4x-8=0

We add all the numbers together, and all the variables

4x^2-5x-8=0

a = 4; b = -5; c = -8;
Δ = b2-4ac
Δ = -52-4·4·(-8)
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{17}}{2*4}=\frac{5-3\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{17}}{2*4}=\frac{5+3\sqrt{17}}{8}
$