3x(x-5)=24

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

3x(x-5)=24

We move all terms to the left:

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

We multiply parentheses

3x^2-15x-24=0

a = 3; b = -15; c = -24;
Δ = b2-4ac
Δ = -152-4·3·(-24)
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{57}}{2*3}=\frac{15-3\sqrt{57}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{57}}{2*3}=\frac{15+3\sqrt{57}}{6}
$