2y^2-16y+64=35

Solution for 2y^2-16y+64=35 equation:

2y^2-16y+64=35

We move all terms to the left:

2y^2-16y+64-(35)=0

We add all the numbers together, and all the variables

2y^2-16y+29=0

a = 2; b = -16; c = +29;
Δ = b2-4ac
Δ = -162-4·2·29
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{6}}{2*2}=\frac{16-2\sqrt{6}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{6}}{2*2}=\frac{16+2\sqrt{6}}{4}
$