3x(x+42)=180

Solution for 3x(x+42)=180 equation:

3x(x+42)=180

We move all terms to the left:

3x(x+42)-(180)=0

We multiply parentheses

3x^2+126x-180=0

a = 3; b = 126; c = -180;
Δ = b2-4ac
Δ = 1262-4·3·(-180)
Δ = 18036
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:

$\sqrt{\Delta}=\sqrt{18036}=\sqrt{36*501}=\sqrt{36}*\sqrt{501}=6\sqrt{501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-6\sqrt{501}}{2*3}=\frac{-126-6\sqrt{501}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+6\sqrt{501}}{2*3}=\frac{-126+6\sqrt{501}}{6}
$