2y^2+2y=21.5

Solution for 2y^2+2y=21.5 equation:

2y^2+2y=21.5

We move all terms to the left:

2y^2+2y-(21.5)=0

We add all the numbers together, and all the variables

2y^2+2y-21.5=0

a = 2; b = 2; c = -21.5;
Δ = b2-4ac
Δ = 22-4·2·(-21.5)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{11}}{2*2}=\frac{-2-4\sqrt{11}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{11}}{2*2}=\frac{-2+4\sqrt{11}}{4}
$