y^2-3y=8

Solution for y^2-3y=8 equation:

y^2-3y=8

We move all terms to the left:

y^2-3y-(8)=0

a = 1; b = -3; c = -8;
Δ = b2-4ac
Δ = -32-4·1·(-8)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{41}}{2*1}=\frac{3-\sqrt{41}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{41}}{2*1}=\frac{3+\sqrt{41}}{2}
$