2x(3x+21)=180

Solution for 2x(3x+21)=180 equation:

2x(3x+21)=180

We move all terms to the left:

2x(3x+21)-(180)=0

We multiply parentheses

6x^2+42x-180=0

a = 6; b = 42; c = -180;
Δ = b2-4ac
Δ = 422-4·6·(-180)
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-78}{2*6}=\frac{-120}{12}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+78}{2*6}=\frac{36}{12}
=3
$