-24/2+30/6x=3x-6

Solution for -24/2+30/6x=3x-6 equation:

-24/2+30/6x=3x-6

We move all terms to the left:

-24/2+30/6x-(3x-6)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

30/6x-(3x-6)-12=0

We get rid of parentheses

30/6x-3x+6-12=0

We multiply all the terms by the denominator


-3x*6x+6*6x-12*6x+30=0

Wy multiply elements

-18x^2+36x-72x+30=0

We add all the numbers together, and all the variables

-18x^2-36x+30=0

a = -18; b = -36; c = +30;
Δ = b2-4ac
Δ = -362-4·(-18)·30
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-24\sqrt{6}}{2*-18}=\frac{36-24\sqrt{6}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+24\sqrt{6}}{2*-18}=\frac{36+24\sqrt{6}}{-36}
$