(10+y)(y)=17

Solution for (10+y)(y)=17 equation:

(10+y)(y)=17

We move all terms to the left:

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

We add all the numbers together, and all the variables

(y+10)y-17=0

We multiply parentheses

y^2+10y-17=0

a = 1; b = 10; c = -17;
Δ = b2-4ac
Δ = 102-4·1·(-17)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{42}}{2*1}=\frac{-10-2\sqrt{42}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{42}}{2*1}=\frac{-10+2\sqrt{42}}{2}
$