3x(2x+30)=180

Solution for 3x(2x+30)=180 equation:

3x(2x+30)=180

We move all terms to the left:

3x(2x+30)-(180)=0

We multiply parentheses

6x^2+90x-180=0

a = 6; b = 90; c = -180;
Δ = b2-4ac
Δ = 902-4·6·(-180)
Δ = 12420
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:

$\sqrt{\Delta}=\sqrt{12420}=\sqrt{36*345}=\sqrt{36}*\sqrt{345}=6\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{345}}{2*6}=\frac{-90-6\sqrt{345}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{345}}{2*6}=\frac{-90+6\sqrt{345}}{12}
$