(10x+5)(12x-5)=180

Solution for (10x+5)(12x-5)=180 equation:

(10x+5)(12x-5)=180

We move all terms to the left:

(10x+5)(12x-5)-(180)=0

We multiply parentheses ..

(+120x^2-50x+60x-25)-180=0

We get rid of parentheses

120x^2-50x+60x-25-180=0

We add all the numbers together, and all the variables

120x^2+10x-205=0

a = 120; b = 10; c = -205;
Δ = b2-4ac
Δ = 102-4·120·(-205)
Δ = 98500
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:

$\sqrt{\Delta}=\sqrt{98500}=\sqrt{100*985}=\sqrt{100}*\sqrt{985}=10\sqrt{985}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{985}}{2*120}=\frac{-10-10\sqrt{985}}{240}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{985}}{2*120}=\frac{-10+10\sqrt{985}}{240}
$