180=78x-6x^2

Solution for 180=78x-6x^2 equation:

180=78x-6x^2

We move all terms to the left:

180-(78x-6x^2)=0

We get rid of parentheses

6x^2-78x+180=0

a = 6; b = -78; c = +180;
Δ = b2-4ac
Δ = -782-4·6·180
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-42}{2*6}=\frac{36}{12}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+42}{2*6}=\frac{120}{12}
=10
$