1/2x+14=1/4x-22

Solution for 1/2x+14=1/4x-22 equation:

1/2x+14=1/4x-22

We move all terms to the left:

1/2x+14-(1/4x-22)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-22)!=0

x∈R


We get rid of parentheses

1/2x-1/4x+22+14=0

We calculate fractions


4x/8x^2+(-2x)/8x^2+22+14=0

We add all the numbers together, and all the variables

4x/8x^2+(-2x)/8x^2+36=0

We multiply all the terms by the denominator


4x+(-2x)+36*8x^2=0

Wy multiply elements

288x^2+4x+(-2x)=0

We get rid of parentheses

288x^2+4x-2x=0

We add all the numbers together, and all the variables

288x^2+2x=0

a = 288; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·288·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*288}=\frac{-4}{576}
=-1/144
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*288}=\frac{0}{576}
=0
$