4x(2x-3)=23

Solution for 4x(2x-3)=23 equation:

4x(2x-3)=23

We move all terms to the left:

4x(2x-3)-(23)=0

We multiply parentheses

8x^2-12x-23=0

a = 8; b = -12; c = -23;
Δ = b2-4ac
Δ = -122-4·8·(-23)
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{55}}{2*8}=\frac{12-4\sqrt{55}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{55}}{2*8}=\frac{12+4\sqrt{55}}{16}
$