24x^2-18x+12+15x-30=0+0+0

Solution for 24x^2-18x+12+15x-30=0+0+0 equation:

24x^2-18x+12+15x-30=0+0+0

We move all terms to the left:

24x^2-18x+12+15x-30-(0+0+0)=0

We add all the numbers together, and all the variables

24x^2-18x+15x+12-30-0=0

We add all the numbers together, and all the variables

24x^2-3x-18=0

a = 24; b = -3; c = -18;
Δ = b2-4ac
Δ = -32-4·24·(-18)
Δ = 1737
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:

$\sqrt{\Delta}=\sqrt{1737}=\sqrt{9*193}=\sqrt{9}*\sqrt{193}=3\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{193}}{2*24}=\frac{3-3\sqrt{193}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{193}}{2*24}=\frac{3+3\sqrt{193}}{48}
$