0.25y^2+0.25y+0.5=8

Solution for 0.25y^2+0.25y+0.5=8 equation:

0.25y^2+0.25y+0.5=8

We move all terms to the left:

0.25y^2+0.25y+0.5-(8)=0

We add all the numbers together, and all the variables

0.25y^2+0.25y-7.5=0

a = 0.25; b = 0.25; c = -7.5;
Δ = b2-4ac
Δ = 0.252-4·0.25·(-7.5)
Δ = 7.5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.25)-\sqrt{7.5625}}{2*0.25}=\frac{-0.25-\sqrt{7.5625}}{0.5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.25)+\sqrt{7.5625}}{2*0.25}=\frac{-0.25+\sqrt{7.5625}}{0.5}
$