88=-x^2+46x-360

Solution for 88=-x^2+46x-360 equation:

88=-x^2+46x-360

We move all terms to the left:

88-(-x^2+46x-360)=0

We get rid of parentheses

x^2-46x+360+88=0

We add all the numbers together, and all the variables

x^2-46x+448=0

a = 1; b = -46; c = +448;
Δ = b2-4ac
Δ = -462-4·1·448
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-18}{2*1}=\frac{28}{2}
=14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+18}{2*1}=\frac{64}{2}
=32
$