2y^2-8y+16=154

Solution for 2y^2-8y+16=154 equation:

2y^2-8y+16=154

We move all terms to the left:

2y^2-8y+16-(154)=0

We add all the numbers together, and all the variables

2y^2-8y-138=0

a = 2; b = -8; c = -138;
Δ = b2-4ac
Δ = -82-4·2·(-138)
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{73}}{2*2}=\frac{8-4\sqrt{73}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{73}}{2*2}=\frac{8+4\sqrt{73}}{4}
$