(25+y)y=17

Solution for (25+y)y=17 equation:

(25+y)y=17

We move all terms to the left:

(25+y)y-(17)=0

We add all the numbers together, and all the variables

(y+25)y-17=0

We multiply parentheses

y^2+25y-17=0

a = 1; b = 25; c = -17;
Δ = b2-4ac
Δ = 252-4·1·(-17)
Δ = 693
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:

$\sqrt{\Delta}=\sqrt{693}=\sqrt{9*77}=\sqrt{9}*\sqrt{77}=3\sqrt{77}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-3\sqrt{77}}{2*1}=\frac{-25-3\sqrt{77}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+3\sqrt{77}}{2*1}=\frac{-25+3\sqrt{77}}{2}
$