1/2x+3=1/4x-2

Solution for 1/2x+3=1/4x-2 equation:

1/2x+3=1/4x-2

We move all terms to the left:

1/2x+3-(1/4x-2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-2)!=0

x∈R


We get rid of parentheses

1/2x-1/4x+2+3=0

We calculate fractions


4x/8x^2+(-2x)/8x^2+2+3=0

We add all the numbers together, and all the variables

4x/8x^2+(-2x)/8x^2+5=0

We multiply all the terms by the denominator


4x+(-2x)+5*8x^2=0

Wy multiply elements

40x^2+4x+(-2x)=0

We get rid of parentheses

40x^2+4x-2x=0

We add all the numbers together, and all the variables

40x^2+2x=0

a = 40; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·40·0
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*40}=\frac{-4}{80}
=-1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*40}=\frac{0}{80}
=0
$