5/4x=9-6x

Solution for 5/4x=9-6x equation:

5/4x=9-6x

We move all terms to the left:

5/4x-(9-6x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5/4x-(-6x+9)=0

We get rid of parentheses

5/4x+6x-9=0

We multiply all the terms by the denominator


6x*4x-9*4x+5=0

Wy multiply elements

24x^2-36x+5=0

a = 24; b = -36; c = +5;
Δ = b2-4ac
Δ = -362-4·24·5
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{51}}{2*24}=\frac{36-4\sqrt{51}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{51}}{2*24}=\frac{36+4\sqrt{51}}{48}
$