(x-4)(x-4)=77

Solution for (x-4)(x-4)=77 equation:

(x-4)(x-4)=77

We move all terms to the left:

(x-4)(x-4)-(77)=0

We multiply parentheses ..

(+x^2-4x-4x+16)-77=0

We get rid of parentheses

x^2-4x-4x+16-77=0

We add all the numbers together, and all the variables

x^2-8x-61=0

a = 1; b = -8; c = -61;
Δ = b2-4ac
Δ = -82-4·1·(-61)
Δ = 308
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{77}}{2*1}=\frac{8-2\sqrt{77}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{77}}{2*1}=\frac{8+2\sqrt{77}}{2}
$