y^2+2y=247

Solution for y^2+2y=247 equation:

y^2+2y=247

We move all terms to the left:

y^2+2y-(247)=0

a = 1; b = 2; c = -247;
Δ = b2-4ac
Δ = 22-4·1·(-247)
Δ = 992
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:

$\sqrt{\Delta}=\sqrt{992}=\sqrt{16*62}=\sqrt{16}*\sqrt{62}=4\sqrt{62}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{62}}{2*1}=\frac{-2-4\sqrt{62}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{62}}{2*1}=\frac{-2+4\sqrt{62}}{2}
$