(10x+1)(12x-5)=180

Solution for (10x+1)(12x-5)=180 equation:

(10x+1)(12x-5)=180

We move all terms to the left:

(10x+1)(12x-5)-(180)=0

We multiply parentheses ..

(+120x^2-50x+12x-5)-180=0

We get rid of parentheses

120x^2-50x+12x-5-180=0

We add all the numbers together, and all the variables

120x^2-38x-185=0

a = 120; b = -38; c = -185;
Δ = b2-4ac
Δ = -382-4·120·(-185)
Δ = 90244
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:

$\sqrt{\Delta}=\sqrt{90244}=\sqrt{4*22561}=\sqrt{4}*\sqrt{22561}=2\sqrt{22561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{22561}}{2*120}=\frac{38-2\sqrt{22561}}{240}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{22561}}{2*120}=\frac{38+2\sqrt{22561}}{240}
$