-2x(6x-15)2/3=-4

Solution for -2x(6x-15)2/3=-4 equation:

-2x(6x-15)2/3=-4

We move all terms to the left:

-2x(6x-15)2/3-(-4)=0

We add all the numbers together, and all the variables

-2x(6x-15)2/3+4=0

We multiply all the terms by the denominator


-2x(6x-15)2+4*3=0

We add all the numbers together, and all the variables

-2x(6x-15)2+12=0

We multiply parentheses

-24x^2+60x+12=0

a = -24; b = 60; c = +12;
Δ = b2-4ac
Δ = 602-4·(-24)·12
Δ = 4752
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:

$\sqrt{\Delta}=\sqrt{4752}=\sqrt{144*33}=\sqrt{144}*\sqrt{33}=12\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-12\sqrt{33}}{2*-24}=\frac{-60-12\sqrt{33}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+12\sqrt{33}}{2*-24}=\frac{-60+12\sqrt{33}}{-48}
$