2x(5x-3)=24

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

2x(5x-3)=24

We move all terms to the left:

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

We multiply parentheses

10x^2-6x-24=0

a = 10; b = -6; c = -24;
Δ = b2-4ac
Δ = -62-4·10·(-24)
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{249}}{2*10}=\frac{6-2\sqrt{249}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{249}}{2*10}=\frac{6+2\sqrt{249}}{20}
$