y^2+5y=75

Solution for y^2+5y=75 equation:

y^2+5y=75

We move all terms to the left:

y^2+5y-(75)=0

a = 1; b = 5; c = -75;
Δ = b2-4ac
Δ = 52-4·1·(-75)
Δ = 325
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{13}}{2*1}=\frac{-5-5\sqrt{13}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{13}}{2*1}=\frac{-5+5\sqrt{13}}{2}
$