1.5x^2-24L-15=0

Solution for 1.5x^2-24L-15=0 equation:

1.5x^2-24-15=0

We add all the numbers together, and all the variables

1.5x^2-39=0

a = 1.5; b = 0; c = -39;
Δ = b2-4ac
Δ = 02-4·1.5·(-39)
Δ = 234
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:

$\sqrt{\Delta}=\sqrt{234}=\sqrt{9*26}=\sqrt{9}*\sqrt{26}=3\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{26}}{2*1.5}=\frac{0-3\sqrt{26}}{3}
=-\frac{3\sqrt{26}}{3}
=-\sqrt{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{26}}{2*1.5}=\frac{0+3\sqrt{26}}{3}
=\frac{3\sqrt{26}}{3}
=\sqrt{26}
$