8x-1/4x=23-4x

Solution for 8x-1/4x=23-4x equation:

8x-1/4x=23-4x

We move all terms to the left:

8x-1/4x-(23-4x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

8x-1/4x-(-4x+23)=0

We get rid of parentheses

8x-1/4x+4x-23=0

We multiply all the terms by the denominator


8x*4x+4x*4x-23*4x-1=0

Wy multiply elements

32x^2+16x^2-92x-1=0

We add all the numbers together, and all the variables

48x^2-92x-1=0

a = 48; b = -92; c = -1;
Δ = b2-4ac
Δ = -922-4·48·(-1)
Δ = 8656
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:

$\sqrt{\Delta}=\sqrt{8656}=\sqrt{16*541}=\sqrt{16}*\sqrt{541}=4\sqrt{541}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-4\sqrt{541}}{2*48}=\frac{92-4\sqrt{541}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+4\sqrt{541}}{2*48}=\frac{92+4\sqrt{541}}{96}
$