18/3+24/3x=8x-12/4

Solution for 18/3+24/3x=8x-12/4 equation:

18/3+24/3x=8x-12/4

We move all terms to the left:

18/3+24/3x-(8x-12/4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

24/3x-(8x-3)+18/3=0

We add all the numbers together, and all the variables

24/3x-(8x-3)+6=0

We get rid of parentheses

24/3x-8x+3+6=0

We multiply all the terms by the denominator


-8x*3x+3*3x+6*3x+24=0

Wy multiply elements

-24x^2+9x+18x+24=0

We add all the numbers together, and all the variables

-24x^2+27x+24=0

a = -24; b = 27; c = +24;
Δ = b2-4ac
Δ = 272-4·(-24)·24
Δ = 3033
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:

$\sqrt{\Delta}=\sqrt{3033}=\sqrt{9*337}=\sqrt{9}*\sqrt{337}=3\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{337}}{2*-24}=\frac{-27-3\sqrt{337}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{337}}{2*-24}=\frac{-27+3\sqrt{337}}{-48}
$