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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

We move all terms containing x to the left, all other terms to the right

x+2)!=2

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

Fractions to decimals

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

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2-8x+2x-3=0

We add all the numbers together, and all the variables

2x^2-6x-3=0

a = 2; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·2·(-3)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{15}}{2*2}=\frac{6-2\sqrt{15}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{15}}{2*2}=\frac{6+2\sqrt{15}}{4}
$