9/4x=2x+9

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

9/4x=2x+9

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

9/4x-2x-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}
$