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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


6x/8x^2+(-4x)/8x^2+2+3=0

We add all the numbers together, and all the variables

6x/8x^2+(-4x)/8x^2+5=0

We multiply all the terms by the denominator


6x+(-4x)+5*8x^2=0

Wy multiply elements

40x^2+6x+(-4x)=0

We get rid of parentheses

40x^2+6x-4x=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
$