x^2+89=19x-1

Solution for x^2+89=19x-1 equation:

x^2+89=19x-1

We move all terms to the left:

x^2+89-(19x-1)=0

We get rid of parentheses

x^2-19x+1+89=0

We add all the numbers together, and all the variables

x^2-19x+90=0

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

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-1}{2*1}=\frac{18}{2}
=9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+1}{2*1}=\frac{20}{2}
=10
$