(3x+23)(4x)=180

Solution for (3x+23)(4x)=180 equation:

(3x+23)(4x)=180

We move all terms to the left:

(3x+23)(4x)-(180)=0

We multiply parentheses

12x^2+92x-180=0

a = 12; b = 92; c = -180;
Δ = b2-4ac
Δ = 922-4·12·(-180)
Δ = 17104
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:

$\sqrt{\Delta}=\sqrt{17104}=\sqrt{16*1069}=\sqrt{16}*\sqrt{1069}=4\sqrt{1069}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-4\sqrt{1069}}{2*12}=\frac{-92-4\sqrt{1069}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+4\sqrt{1069}}{2*12}=\frac{-92+4\sqrt{1069}}{24}
$