3x(x-10)=180

Solution for 3x(x-10)=180 equation:

3x(x-10)=180

We move all terms to the left:

3x(x-10)-(180)=0

We multiply parentheses

3x^2-30x-180=0

a = 3; b = -30; c = -180;
Δ = b2-4ac
Δ = -302-4·3·(-180)
Δ = 3060
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:

$\sqrt{\Delta}=\sqrt{3060}=\sqrt{36*85}=\sqrt{36}*\sqrt{85}=6\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{85}}{2*3}=\frac{30-6\sqrt{85}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{85}}{2*3}=\frac{30+6\sqrt{85}}{6}
$