(x-5)(x-5)=112,78

Solution for (x-5)(x-5)=112,78 equation:

(x-5)(x-5)=112.78

We move all terms to the left:

(x-5)(x-5)-(112.78)=0

We add all the numbers together, and all the variables

(x-5)(x-5)-112.78=0

We multiply parentheses ..

(+x^2-5x-5x+25)-112.78=0

We get rid of parentheses

x^2-5x-5x+25-112.78=0

We add all the numbers together, and all the variables

x^2-10x-87.78=0

a = 1; b = -10; c = -87.78;
Δ = b2-4ac
Δ = -102-4·1·(-87.78)
Δ = 451.12
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{-(-10)-\sqrt{451.12}}{2*1}=\frac{10-\sqrt{451.12}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+\sqrt{451.12}}{2*1}=\frac{10+\sqrt{451.12}}{2}
$