2x=9/4x+9

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

2x=9/4x+9

We move all terms to the left:

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


Domain of the equation: 4x+9)!=0

x∈R


We get rid of parentheses

2x-9/4x-9=0

We multiply all the terms by the denominator


2x*4x-9*4x-9=0

Wy multiply elements

8x^2-36x-9=0

a = 8; b = -36; c = -9;
Δ = b2-4ac
Δ = -362-4·8·(-9)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{11}}{2*8}=\frac{36-12\sqrt{11}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{11}}{2*8}=\frac{36+12\sqrt{11}}{16}
$