(y-4)*(y-4)=26

Solution for (y-4)*(y-4)=26 equation:

(y-4)(y-4)=26

We move all terms to the left:

(y-4)(y-4)-(26)=0

We multiply parentheses ..

(+y^2-4y-4y+16)-26=0

We get rid of parentheses

y^2-4y-4y+16-26=0

We add all the numbers together, and all the variables

y^2-8y-10=0

a = 1; b = -8; c = -10;
Δ = b2-4ac
Δ = -82-4·1·(-10)
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*1}=\frac{8-2\sqrt{26}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{26}}{2*1}=\frac{8+2\sqrt{26}}{2}
$