3x+9/4x-4=2

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

3x+9/4x-4=2

We move all terms to the left:

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

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-24x+9=0

a = 12; b = -24; c = +9;
Δ = b2-4ac
Δ = -242-4·12·9
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12}{2*12}=\frac{12}{24}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12}{2*12}=\frac{36}{24}
=1+1/2
$