(x-7)(x-7)=100

Solution for (x-7)(x-7)=100 equation:

(x-7)(x-7)=100

We move all terms to the left:

(x-7)(x-7)-(100)=0

We multiply parentheses ..

(+x^2-7x-7x+49)-100=0

We get rid of parentheses

x^2-7x-7x+49-100=0

We add all the numbers together, and all the variables

x^2-14x-51=0

a = 1; b = -14; c = -51;
Δ = b2-4ac
Δ = -142-4·1·(-51)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-20}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+20}{2*1}=\frac{34}{2}
=17
$