(15/4*y+15)y=120

Solution for (15/4*y+15)y=120 equation:

(15/4y+15)y=120

We move all terms to the left:

(15/4y+15)y-(120)=0


Domain of the equation: 4y+15)y!=0

y∈R


We multiply parentheses

15y^2+15y-120=0

a = 15; b = 15; c = -120;
Δ = b2-4ac
Δ = 152-4·15·(-120)
Δ = 7425
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:

$\sqrt{\Delta}=\sqrt{7425}=\sqrt{225*33}=\sqrt{225}*\sqrt{33}=15\sqrt{33}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15\sqrt{33}}{2*15}=\frac{-15-15\sqrt{33}}{30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15\sqrt{33}}{2*15}=\frac{-15+15\sqrt{33}}{30}
$