(X-5)(x-5)=14

Solution for (X-5)(x-5)=14 equation:

(X-5)(X-5)=14

We move all terms to the left:

(X-5)(X-5)-(14)=0

We multiply parentheses ..

(+X^2-5X-5X+25)-14=0

We get rid of parentheses

X^2-5X-5X+25-14=0

We add all the numbers together, and all the variables

X^2-10X+11=0

a = 1; b = -10; c = +11;
Δ = b2-4ac
Δ = -102-4·1·11
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{14}}{2*1}=\frac{10-2\sqrt{14}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{14}}{2*1}=\frac{10+2\sqrt{14}}{2}
$