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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+120x^2-100x+96x-80)-180=0

We get rid of parentheses

120x^2-100x+96x-80-180=0

We add all the numbers together, and all the variables

120x^2-4x-260=0

a = 120; b = -4; c = -260;
Δ = b2-4ac
Δ = -42-4·120·(-260)
Δ = 124816
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:

$\sqrt{\Delta}=\sqrt{124816}=\sqrt{16*7801}=\sqrt{16}*\sqrt{7801}=4\sqrt{7801}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{7801}}{2*120}=\frac{4-4\sqrt{7801}}{240}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{7801}}{2*120}=\frac{4+4\sqrt{7801}}{240}
$