x^2=19x+90=0

Solution for x^2=19x+90=0 equation:

x^2=19x+90=0

We move all terms to the left:

x^2-(19x+90)=0

We get rid of parentheses

x^2-19x-90=0

a = 1; b = -19; c = -90;
Δ = b2-4ac
Δ = -192-4·1·(-90)
Δ = 721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{721}}{2*1}=\frac{19-\sqrt{721}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{721}}{2*1}=\frac{19+\sqrt{721}}{2}
$