3x(x-2)-4(2x+5)=24

Solution for 3x(x-2)-4(2x+5)=24 equation:

3x(x-2)-4(2x+5)=24

We move all terms to the left:

3x(x-2)-4(2x+5)-(24)=0

We multiply parentheses

3x^2-6x-8x-20-24=0

We add all the numbers together, and all the variables

3x^2-14x-44=0

a = 3; b = -14; c = -44;
Δ = b2-4ac
Δ = -142-4·3·(-44)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{181}}{2*3}=\frac{14-2\sqrt{181}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{181}}{2*3}=\frac{14+2\sqrt{181}}{6}
$