(2x+3)(2x-3)=101

Solution for (2x+3)(2x-3)=101 equation:

(2x+3)(2x-3)=101

We move all terms to the left:

(2x+3)(2x-3)-(101)=0

We use the square of the difference formula

4x^2-9-101=0

We add all the numbers together, and all the variables

4x^2-110=0

a = 4; b = 0; c = -110;
Δ = b2-4ac
Δ = 02-4·4·(-110)
Δ = 1760
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:

$\sqrt{\Delta}=\sqrt{1760}=\sqrt{16*110}=\sqrt{16}*\sqrt{110}=4\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{110}}{2*4}=\frac{0-4\sqrt{110}}{8}
=-\frac{4\sqrt{110}}{8}
=-\frac{\sqrt{110}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{110}}{2*4}=\frac{0+4\sqrt{110}}{8}
=\frac{4\sqrt{110}}{8}
=\frac{\sqrt{110}}{2}
$