y2+8y=65

Solution for y2+8y=65 equation:

y2+8y=65

We move all terms to the left:

y2+8y-(65)=0

We add all the numbers together, and all the variables

y^2+8y-65=0

a = 1; b = 8; c = -65;
Δ = b2-4ac
Δ = 82-4·1·(-65)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-18}{2*1}=\frac{-26}{2}
=-13
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+18}{2*1}=\frac{10}{2}
=5
$