3(x-6)5x=24

Solution for 3(x-6)5x=24 equation:

3(x-6)5x=24

We move all terms to the left:

3(x-6)5x-(24)=0

We multiply parentheses

15x^2-90x-24=0

a = 15; b = -90; c = -24;
Δ = b2-4ac
Δ = -902-4·15·(-24)
Δ = 9540
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:

$\sqrt{\Delta}=\sqrt{9540}=\sqrt{36*265}=\sqrt{36}*\sqrt{265}=6\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{265}}{2*15}=\frac{90-6\sqrt{265}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{265}}{2*15}=\frac{90+6\sqrt{265}}{30}
$