(7-2x)(7+2x)=6

Solution for (7-2x)(7+2x)=6 equation:

(7-2x)(7+2x)=6

We move all terms to the left:

(7-2x)(7+2x)-(6)=0

We add all the numbers together, and all the variables

(-2x+7)(2x+7)-6=0

We multiply parentheses ..

(-4x^2-14x+14x+49)-6=0

We get rid of parentheses

-4x^2-14x+14x+49-6=0

We add all the numbers together, and all the variables

-4x^2+43=0

a = -4; b = 0; c = +43;
Δ = b2-4ac
Δ = 02-4·(-4)·43
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{43}}{2*-4}=\frac{0-4\sqrt{43}}{-8}
=-\frac{4\sqrt{43}}{-8}
=-\frac{\sqrt{43}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{43}}{2*-4}=\frac{0+4\sqrt{43}}{-8}
=\frac{4\sqrt{43}}{-8}
=\frac{\sqrt{43}}{-2}
$