y^2-19y=-84

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

y^2-19y=-84

We move all terms to the left:

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

We add all the numbers together, and all the variables

y^2-19y+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:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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