U(x)=-6x^2+132x

Solution for U(x)=-6x^2+132x equation:

(U)=-6U^2+132U

We move all terms to the left:

(U)-(-6U^2+132U)=0

We get rid of parentheses

6U^2-132U+U=0

We add all the numbers together, and all the variables

6U^2-131U=0

a = 6; b = -131; c = 0;
Δ = b2-4ac
Δ = -1312-4·6·0
Δ = 17161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17161}=131$
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-131)-131}{2*6}=\frac{0}{12}
=0
$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-131)+131}{2*6}=\frac{262}{12}
=21+5/6
$