(8x+12)(10x+6)=180

Solution for (8x+12)(10x+6)=180 equation:

(8x+12)(10x+6)=180

We move all terms to the left:

(8x+12)(10x+6)-(180)=0

We multiply parentheses ..

(+80x^2+48x+120x+72)-180=0

We get rid of parentheses

80x^2+48x+120x+72-180=0

We add all the numbers together, and all the variables

80x^2+168x-108=0

a = 80; b = 168; c = -108;
Δ = b2-4ac
Δ = 1682-4·80·(-108)
Δ = 62784
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:

$\sqrt{\Delta}=\sqrt{62784}=\sqrt{576*109}=\sqrt{576}*\sqrt{109}=24\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-24\sqrt{109}}{2*80}=\frac{-168-24\sqrt{109}}{160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+24\sqrt{109}}{2*80}=\frac{-168+24\sqrt{109}}{160}
$