2y^2-8y=5

Solution for 2y^2-8y=5 equation:

2y^2-8y=5

We move all terms to the left:

2y^2-8y-(5)=0

a = 2; b = -8; c = -5;
Δ = b2-4ac
Δ = -82-4·2·(-5)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{26}}{2*2}=\frac{8-2\sqrt{26}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{26}}{2*2}=\frac{8+2\sqrt{26}}{4}
$