90=x^2+-5x+54

Solution for 90=x^2+-5x+54 equation:

90=x^2+-5x+54

We move all terms to the left:

90-(x^2+-5x+54)=0

We use the square of the difference formula

-(x^2-5x+54)+90=0

We get rid of parentheses

-x^2+5x-54+90=0

We add all the numbers together, and all the variables

-1x^2+5x+36=0

a = -1; b = 5; c = +36;
Δ = b2-4ac
Δ = 52-4·(-1)·36
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-13}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+13}{2*-1}=\frac{8}{-2}
=-4
$