(X+7)(x+7)=169

Solution for (X+7)(x+7)=169 equation:

(X+7)(X+7)=169

We move all terms to the left:

(X+7)(X+7)-(169)=0

We multiply parentheses ..

(+X^2+7X+7X+49)-169=0

We get rid of parentheses

X^2+7X+7X+49-169=0

We add all the numbers together, and all the variables

X^2+14X-120=0

a = 1; b = 14; c = -120;
Δ = b2-4ac
Δ = 142-4·1·(-120)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-26}{2*1}=\frac{-40}{2}
=-20
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+26}{2*1}=\frac{12}{2}
=6
$