(5x+1)(12x-42)=180

Solution for (5x+1)(12x-42)=180 equation:

(5x+1)(12x-42)=180

We move all terms to the left:

(5x+1)(12x-42)-(180)=0

We multiply parentheses ..

(+60x^2-210x+12x-42)-180=0

We get rid of parentheses

60x^2-210x+12x-42-180=0

We add all the numbers together, and all the variables

60x^2-198x-222=0

a = 60; b = -198; c = -222;
Δ = b2-4ac
Δ = -1982-4·60·(-222)
Δ = 92484
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:

$\sqrt{\Delta}=\sqrt{92484}=\sqrt{36*2569}=\sqrt{36}*\sqrt{2569}=6\sqrt{2569}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-198)-6\sqrt{2569}}{2*60}=\frac{198-6\sqrt{2569}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-198)+6\sqrt{2569}}{2*60}=\frac{198+6\sqrt{2569}}{120}
$