150=-6x^2+100x-180.

Solution for 150=-6x^2+100x-180. equation:

150=-6x^2+100x-180.

We move all terms to the left:

150-(-6x^2+100x-180.)=0

We get rid of parentheses

6x^2-100x+180.+150=0

We add all the numbers together, and all the variables

6x^2-100x+330=0

a = 6; b = -100; c = +330;
Δ = b2-4ac
Δ = -1002-4·6·330
Δ = 2080
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:

$\sqrt{\Delta}=\sqrt{2080}=\sqrt{16*130}=\sqrt{16}*\sqrt{130}=4\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{130}}{2*6}=\frac{100-4\sqrt{130}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{130}}{2*6}=\frac{100+4\sqrt{130}}{12}
$