x^2=19x-84

Solution for x^2=19x-84 equation:

x^2=19x-84

We move all terms to the left:

x^2-(19x-84)=0

We get rid of parentheses

x^2-19x+84=0

a = 1; b = -19; c = +84;
Δ = b2-4ac
Δ = -192-4·1·84
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-5}{2*1}=\frac{14}{2}
=7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+5}{2*1}=\frac{24}{2}
=12
$