(2x-3)(2x)=44

Solution for (2x-3)(2x)=44 equation:

(2x-3)(2x)=44

We move all terms to the left:

(2x-3)(2x)-(44)=0

We multiply parentheses

4x^2-6x-44=0

a = 4; b = -6; c = -44;
Δ = b2-4ac
Δ = -62-4·4·(-44)
Δ = 740
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:

$\sqrt{\Delta}=\sqrt{740}=\sqrt{4*185}=\sqrt{4}*\sqrt{185}=2\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{185}}{2*4}=\frac{6-2\sqrt{185}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{185}}{2*4}=\frac{6+2\sqrt{185}}{8}
$