(X-7)(x-7)=195

Solution for (X-7)(x-7)=195 equation:

(X-7)(X-7)=195

We move all terms to the left:

(X-7)(X-7)-(195)=0

We multiply parentheses ..

(+X^2-7X-7X+49)-195=0

We get rid of parentheses

X^2-7X-7X+49-195=0

We add all the numbers together, and all the variables

X^2-14X-146=0

a = 1; b = -14; c = -146;
Δ = b2-4ac
Δ = -142-4·1·(-146)
Δ = 780
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:

$\sqrt{\Delta}=\sqrt{780}=\sqrt{4*195}=\sqrt{4}*\sqrt{195}=2\sqrt{195}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{195}}{2*1}=\frac{14-2\sqrt{195}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{195}}{2*1}=\frac{14+2\sqrt{195}}{2}
$