X^2-19x+90=20

Solution for X^2-19x+90=20 equation:

X^2-19X+90=20

We move all terms to the left:

X^2-19X+90-(20)=0

We add all the numbers together, and all the variables

X^2-19X+70=0

a = 1; b = -19; c = +70;
Δ = b2-4ac
Δ = -192-4·1·70
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-9}{2*1}=\frac{10}{2}
=5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+9}{2*1}=\frac{28}{2}
=14
$