4x=9-1/4x

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

4x=9-1/4x

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4x+1/4x-9=0

We multiply all the terms by the denominator


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

Wy multiply elements

16x^2-36x+1=0

a = 16; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·16·1
Δ = 1232
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:

$\sqrt{\Delta}=\sqrt{1232}=\sqrt{16*77}=\sqrt{16}*\sqrt{77}=4\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{77}}{2*16}=\frac{36-4\sqrt{77}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{77}}{2*16}=\frac{36+4\sqrt{77}}{32}
$