3x+9/4x=9

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

3x+9/4x=9

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-36x+9=0

a = 12; b = -36; c = +9;
Δ = b2-4ac
Δ = -362-4·12·9
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{6}}{2*12}=\frac{36-12\sqrt{6}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{6}}{2*12}=\frac{36+12\sqrt{6}}{24}
$