(x-3)(x-3)=126.5625

Solution for (x-3)(x-3)=126.5625 equation:

(x-3)(x-3)=126.5625

We move all terms to the left:

(x-3)(x-3)-(126.5625)=0

We add all the numbers together, and all the variables

(x-3)(x-3)-126.5625=0

We multiply parentheses ..

(+x^2-3x-3x+9)-126.5625=0

We get rid of parentheses

x^2-3x-3x+9-126.5625=0

We add all the numbers together, and all the variables

x^2-6x-117.5625=0

a = 1; b = -6; c = -117.5625;
Δ = b2-4ac
Δ = -62-4·1·(-117.5625)
Δ = 506.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-\sqrt{506.25}}{2*1}=\frac{6-\sqrt{506.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+\sqrt{506.25}}{2*1}=\frac{6+\sqrt{506.25}}{2}
$