4x^2-7x-12=4x-8

Solution for 4x^2-7x-12=4x-8 equation:

4x^2-7x-12=4x-8

We move all terms to the left:

4x^2-7x-12-(4x-8)=0

We get rid of parentheses

4x^2-7x-4x+8-12=0

We add all the numbers together, and all the variables

4x^2-11x-4=0

a = 4; b = -11; c = -4;
Δ = b2-4ac
Δ = -112-4·4·(-4)
Δ = 185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{185}}{2*4}=\frac{11-\sqrt{185}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{185}}{2*4}=\frac{11+\sqrt{185}}{8}
$