2x=3X-9/4X-6

Solution for 2x=3X-9/4X-6 equation:

2x=3x-9/4x-6

We move all terms to the left:

2x-(3x-9/4x-6)=0


Domain of the equation: 4x-6)!=0

x∈R


We get rid of parentheses

2x-3x+9/4x+6=0

We multiply all the terms by the denominator


2x*4x-3x*4x+6*4x+9=0

Wy multiply elements

8x^2-12x^2+24x+9=0

We add all the numbers together, and all the variables

-4x^2+24x+9=0

a = -4; b = 24; c = +9;
Δ = b2-4ac
Δ = 242-4·(-4)·9
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12\sqrt{5}}{2*-4}=\frac{-24-12\sqrt{5}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{5}}{2*-4}=\frac{-24+12\sqrt{5}}{-8}
$