9-1/4x=x

Solution for 9-1/4x=x equation:

9-1/4x=x

We move all terms to the left:

9-1/4x-(x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1x-1/4x+9=0

We multiply all the terms by the denominator


-1x*4x+9*4x-1=0

Wy multiply elements

-4x^2+36x-1=0

a = -4; b = 36; c = -1;
Δ = b2-4ac
Δ = 362-4·(-4)·(-1)
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-16\sqrt{5}}{2*-4}=\frac{-36-16\sqrt{5}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+16\sqrt{5}}{2*-4}=\frac{-36+16\sqrt{5}}{-8}
$