(x-5)(x-5)=17.5

Solution for (x-5)(x-5)=17.5 equation:

(x-5)(x-5)=17.5

We move all terms to the left:

(x-5)(x-5)-(17.5)=0

We add all the numbers together, and all the variables

(x-5)(x-5)-17.5=0

We multiply parentheses ..

(+x^2-5x-5x+25)-17.5=0

We get rid of parentheses

x^2-5x-5x+25-17.5=0

We add all the numbers together, and all the variables

x^2-10x+7.5=0

a = 1; b = -10; c = +7.5;
Δ = b2-4ac
Δ = -102-4·1·7.5
Δ = 70
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{70}}{2*1}=\frac{10-\sqrt{70}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+\sqrt{70}}{2*1}=\frac{10+\sqrt{70}}{2}
$