18x=x^2-19

Solution for 18x=x^2-19 equation:

18x=x^2-19

We move all terms to the left:

18x-(x^2-19)=0

We get rid of parentheses

-x^2+18x+19=0

We add all the numbers together, and all the variables

-1x^2+18x+19=0

a = -1; b = 18; c = +19;
Δ = b2-4ac
Δ = 182-4·(-1)·19
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-20}{2*-1}=\frac{-38}{-2}
=+19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+20}{2*-1}=\frac{2}{-2}
=-1
$