x2+18=19x

Solution for x2+18=19x equation:

x2+18=19x

We move all terms to the left:

x2+18-(19x)=0

We add all the numbers together, and all the variables

x^2-19x+18=0

a = 1; b = -19; c = +18;
Δ = b2-4ac
Δ = -192-4·1·18
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-17}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+17}{2*1}=\frac{36}{2}
=18
$