(2y-20)4+(y)2=720

Solution for (2y-20)4+(y)2=720 equation:

(2y-20)4+(y)2=720

We move all terms to the left:

(2y-20)4+(y)2-(720)=0

We add all the numbers together, and all the variables

y^2+(2y-20)4-720=0

We multiply parentheses

y^2+8y-80-720=0

We add all the numbers together, and all the variables

y^2+8y-800=0

a = 1; b = 8; c = -800;
Δ = b2-4ac
Δ = 82-4·1·(-800)
Δ = 3264
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:

$\sqrt{\Delta}=\sqrt{3264}=\sqrt{64*51}=\sqrt{64}*\sqrt{51}=8\sqrt{51}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{51}}{2*1}=\frac{-8-8\sqrt{51}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{51}}{2*1}=\frac{-8+8\sqrt{51}}{2}
$