1/4x+1/2x=1/4x+44

Solution for 1/4x+1/2x=1/4x+44 equation:

1/4x+1/2x=1/4x+44

We move all terms to the left:

1/4x+1/2x-(1/4x+44)=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+44)!=0

x∈R


We get rid of parentheses

1/4x+1/2x-1/4x-44=0

We calculate fractions


(-2x+1)/8x^2+4x/8x^2-44=0

We multiply all the terms by the denominator


(-2x+1)+4x-44*8x^2=0

We add all the numbers together, and all the variables

4x+(-2x+1)-44*8x^2=0

Wy multiply elements

-352x^2+4x+(-2x+1)=0

We get rid of parentheses

-352x^2+4x-2x+1=0

We add all the numbers together, and all the variables

-352x^2+2x+1=0

a = -352; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-352)·1
Δ = 1412
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:

$\sqrt{\Delta}=\sqrt{1412}=\sqrt{4*353}=\sqrt{4}*\sqrt{353}=2\sqrt{353}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{353}}{2*-352}=\frac{-2-2\sqrt{353}}{-704}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{353}}{2*-352}=\frac{-2+2\sqrt{353}}{-704}
$