2*3/4x+24=3x

Solution for 2*3/4x+24=3x equation:

2*3/4x+24=3x

We move all terms to the left:

2*3/4x+24-(3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+2*3/4x+24=0

We multiply all the terms by the denominator


-3x*4x+24*4x+2*3=0

We add all the numbers together, and all the variables

-3x*4x+24*4x+6=0

Wy multiply elements

-12x^2+96x+6=0

a = -12; b = 96; c = +6;
Δ = b2-4ac
Δ = 962-4·(-12)·6
Δ = 9504
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:

$\sqrt{\Delta}=\sqrt{9504}=\sqrt{144*66}=\sqrt{144}*\sqrt{66}=12\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-12\sqrt{66}}{2*-12}=\frac{-96-12\sqrt{66}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+12\sqrt{66}}{2*-12}=\frac{-96+12\sqrt{66}}{-24}
$