0=180-10x^2+30x

Solution for 0=180-10x^2+30x equation:

0=180-10x^2+30x

We move all terms to the left:

0-(180-10x^2+30x)=0

We add all the numbers together, and all the variables

-(180-10x^2+30x)=0

We get rid of parentheses

10x^2-30x-180=0

a = 10; b = -30; c = -180;
Δ = b2-4ac
Δ = -302-4·10·(-180)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-90}{2*10}=\frac{-60}{20}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+90}{2*10}=\frac{120}{20}
=6
$