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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(2x+1)/8x^2+20x/8x^2-4=0

We multiply all the terms by the denominator


(2x+1)+20x-4*8x^2=0

We add all the numbers together, and all the variables

20x+(2x+1)-4*8x^2=0

Wy multiply elements

-32x^2+20x+(2x+1)=0

We get rid of parentheses

-32x^2+20x+2x+1=0

We add all the numbers together, and all the variables

-32x^2+22x+1=0

a = -32; b = 22; c = +1;
Δ = b2-4ac
Δ = 222-4·(-32)·1
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-6\sqrt{17}}{2*-32}=\frac{-22-6\sqrt{17}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+6\sqrt{17}}{2*-32}=\frac{-22+6\sqrt{17}}{-64}
$