(X-5)(x+5)=84

Solution for (X-5)(x+5)=84 equation:

(X-5)(X+5)=84

We move all terms to the left:

(X-5)(X+5)-(84)=0

We use the square of the difference formula

X^2-25-84=0

We add all the numbers together, and all the variables

X^2-109=0

a = 1; b = 0; c = -109;
Δ = b2-4ac
Δ = 02-4·1·(-109)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{109}}{2*1}=\frac{0-2\sqrt{109}}{2}
=-\frac{2\sqrt{109}}{2}
=-\sqrt{109}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{109}}{2*1}=\frac{0+2\sqrt{109}}{2}
=\frac{2\sqrt{109}}{2}
=\sqrt{109}
$