5y^2+3y=120

Solution for 5y^2+3y=120 equation:

5y^2+3y=120

We move all terms to the left:

5y^2+3y-(120)=0

a = 5; b = 3; c = -120;
Δ = b2-4ac
Δ = 32-4·5·(-120)
Δ = 2409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{2409}}{2*5}=\frac{-3-\sqrt{2409}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{2409}}{2*5}=\frac{-3+\sqrt{2409}}{10}
$