(8x-3)(5x+12)=18

Solution for (8x-3)(5x+12)=18 equation:

(8x-3)(5x+12)=18

We move all terms to the left:

(8x-3)(5x+12)-(18)=0

We multiply parentheses ..

(+40x^2+96x-15x-36)-18=0

We get rid of parentheses

40x^2+96x-15x-36-18=0

We add all the numbers together, and all the variables

40x^2+81x-54=0

a = 40; b = 81; c = -54;
Δ = b2-4ac
Δ = 812-4·40·(-54)
Δ = 15201
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:

$\sqrt{\Delta}=\sqrt{15201}=\sqrt{9*1689}=\sqrt{9}*\sqrt{1689}=3\sqrt{1689}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-3\sqrt{1689}}{2*40}=\frac{-81-3\sqrt{1689}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+3\sqrt{1689}}{2*40}=\frac{-81+3\sqrt{1689}}{80}
$