y^2+2y=134

Solution for y^2+2y=134 equation:

y^2+2y=134

We move all terms to the left:

y^2+2y-(134)=0

a = 1; b = 2; c = -134;
Δ = b2-4ac
Δ = 22-4·1·(-134)
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{15}}{2*1}=\frac{-2-6\sqrt{15}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{15}}{2*1}=\frac{-2+6\sqrt{15}}{2}
$