2(5)y+5y^2=315

Solution for 2(5)y+5y^2=315 equation:

2(5)y+5y^2=315

We move all terms to the left:

2(5)y+5y^2-(315)=0

a = 5; b = 25; c = -315;
Δ = b2-4ac
Δ = 252-4·5·(-315)
Δ = 6925
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:

$\sqrt{\Delta}=\sqrt{6925}=\sqrt{25*277}=\sqrt{25}*\sqrt{277}=5\sqrt{277}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{277}}{2*5}=\frac{-25-5\sqrt{277}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{277}}{2*5}=\frac{-25+5\sqrt{277}}{10}
$