9-2x=x-3/4x

Solution for 9-2x=x-3/4x equation:

9-2x=x-3/4x

We move all terms to the left:

9-2x-(x-3/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-2x-(+x-3/4x)+9=0

We get rid of parentheses

-2x-x+3/4x+9=0

We multiply all the terms by the denominator


-2x*4x-x*4x+9*4x+3=0

Wy multiply elements

-8x^2-4x^2+36x+3=0

We add all the numbers together, and all the variables

-12x^2+36x+3=0

a = -12; b = 36; c = +3;
Δ = b2-4ac
Δ = 362-4·(-12)·3
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{10}}{2*-12}=\frac{-36-12\sqrt{10}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{10}}{2*-12}=\frac{-36+12\sqrt{10}}{-24}
$