7(x-7)(x+7)=77

Solution for 7(x-7)(x+7)=77 equation:

7(x-7)(x+7)=77

We move all terms to the left:

7(x-7)(x+7)-(77)=0

We use the square of the difference formula

x^2-49-77=0

We add all the numbers together, and all the variables

x^2-126=0

a = 1; b = 0; c = -126;
Δ = b2-4ac
Δ = 02-4·1·(-126)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{14}}{2*1}=\frac{0-6\sqrt{14}}{2}
=-\frac{6\sqrt{14}}{2}
=-3\sqrt{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{14}}{2*1}=\frac{0+6\sqrt{14}}{2}
=\frac{6\sqrt{14}}{2}
=3\sqrt{14}
$