y2+30y-75=100

Solution for y2+30y-75=100 equation:

y2+30y-75=100

We move all terms to the left:

y2+30y-75-(100)=0

We add all the numbers together, and all the variables

y^2+30y-175=0

a = 1; b = 30; c = -175;
Δ = b2-4ac
Δ = 302-4·1·(-175)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-40}{2*1}=\frac{-70}{2}
=-35
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+40}{2*1}=\frac{10}{2}
=5
$