4x(x-6)=7x+8

Solution for 4x(x-6)=7x+8 equation:

4x(x-6)=7x+8

We move all terms to the left:

4x(x-6)-(7x+8)=0

We multiply parentheses

4x^2-24x-(7x+8)=0

We get rid of parentheses

4x^2-24x-7x-8=0

We add all the numbers together, and all the variables

4x^2-31x-8=0

a = 4; b = -31; c = -8;
Δ = b2-4ac
Δ = -312-4·4·(-8)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-33}{2*4}=\frac{-2}{8}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+33}{2*4}=\frac{64}{8}
=8
$