y^2-8y=84

Solution for y^2-8y=84 equation:

y^2-8y=84

We move all terms to the left:

y^2-8y-(84)=0

a = 1; b = -8; c = -84;
Δ = b2-4ac
Δ = -82-4·1·(-84)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-20}{2*1}=\frac{-12}{2}
=-6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+20}{2*1}=\frac{28}{2}
=14
$