U=-x^2+22x-105

Solution for U=-x^2+22x-105 equation:

=-U^2+22U-105

We move all terms to the left:

-(-U^2+22U-105)=0

We get rid of parentheses

U^2-22U+105=0

a = 1; b = -22; c = +105;
Δ = b2-4ac
Δ = -222-4·1·105
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$U_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-8}{2*1}=\frac{14}{2}
=7
$
$U_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+8}{2*1}=\frac{30}{2}
=15
$