15y^2-30=22y+7

Solution for 15y^2-30=22y+7 equation:

15y^2-30=22y+7

We move all terms to the left:

15y^2-30-(22y+7)=0

We get rid of parentheses

15y^2-22y-7-30=0

We add all the numbers together, and all the variables

15y^2-22y-37=0

a = 15; b = -22; c = -37;
Δ = b2-4ac
Δ = -222-4·15·(-37)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-52}{2*15}=\frac{-30}{30}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+52}{2*15}=\frac{74}{30}
=2+7/15
$