0=2x+9/4x-9

Solution for 0=2x+9/4x-9 equation:

0=2x+9/4x-9

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

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 = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{7}}{2*-8}=\frac{-36-12\sqrt{7}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{7}}{2*-8}=\frac{-36+12\sqrt{7}}{-16}
$