-2x+6/1.5x=24

Solution for -2x+6/1.5x=24 equation:

-2x+6/1.5x=24

We move all terms to the left:

-2x+6/1.5x-(24)=0


Domain of the equation: 1.5x!=0

x!=0/1.5

x!=0

x∈R


We multiply all the terms by the denominator


-2x*1.5x-24*1.5x+6=0

Wy multiply elements

-2x^2-24x+6=0

a = -2; b = -24; c = +6;
Δ = b2-4ac
Δ = -242-4·(-2)·6
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{39}}{2*-2}=\frac{24-4\sqrt{39}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{39}}{2*-2}=\frac{24+4\sqrt{39}}{-4}
$