15+5y(5+y)=415

Solution for 15+5y(5+y)=415 equation:

15+5y(5+y)=415

We move all terms to the left:

15+5y(5+y)-(415)=0

We add all the numbers together, and all the variables

5y(y+5)+15-415=0

We add all the numbers together, and all the variables

5y(y+5)-400=0

We multiply parentheses

5y^2+25y-400=0

a = 5; b = 25; c = -400;
Δ = b2-4ac
Δ = 252-4·5·(-400)
Δ = 8625
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:

$\sqrt{\Delta}=\sqrt{8625}=\sqrt{25*345}=\sqrt{25}*\sqrt{345}=5\sqrt{345}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{345}}{2*5}=\frac{-25-5\sqrt{345}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{345}}{2*5}=\frac{-25+5\sqrt{345}}{10}
$