2(4x+5)-3x(x-6)=8

Solution for 2(4x+5)-3x(x-6)=8 equation:

2(4x+5)-3x(x-6)=8

We move all terms to the left:

2(4x+5)-3x(x-6)-(8)=0

We multiply parentheses

-3x^2+8x+18x+10-8=0

We add all the numbers together, and all the variables

-3x^2+26x+2=0

a = -3; b = 26; c = +2;
Δ = b2-4ac
Δ = 262-4·(-3)·2
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-10\sqrt{7}}{2*-3}=\frac{-26-10\sqrt{7}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+10\sqrt{7}}{2*-3}=\frac{-26+10\sqrt{7}}{-6}
$