1/4x-2=6+5/2x

Solution for 1/4x-2=6+5/2x equation:

1/4x-2=6+5/2x

We move all terms to the left:

1/4x-2-(6+5/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(5/2x+6)-2=0

We get rid of parentheses

1/4x-5/2x-6-2=0

We calculate fractions


2x/8x^2+(-20x)/8x^2-6-2=0

We add all the numbers together, and all the variables

2x/8x^2+(-20x)/8x^2-8=0

We multiply all the terms by the denominator


2x+(-20x)-8*8x^2=0

Wy multiply elements

-64x^2+2x+(-20x)=0

We get rid of parentheses

-64x^2+2x-20x=0

We add all the numbers together, and all the variables

-64x^2-18x=0

a = -64; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-64)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-64}=\frac{0}{-128}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-64}=\frac{36}{-128}
=-9/32
$