2/2-3x=-2/4x

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

2/2-3x=-2/4x

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-12x^2+4x+2=0

a = -12; b = 4; c = +2;
Δ = b2-4ac
Δ = 42-4·(-12)·2
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{7}}{2*-12}=\frac{-4-4\sqrt{7}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{7}}{2*-12}=\frac{-4+4\sqrt{7}}{-24}
$