5/2x-2=9/2x-2x+2

Solution for 5/2x-2=9/2x-2x+2 equation:

5/2x-2=9/2x-2x+2

We move all terms to the left:

5/2x-2-(9/2x-2x+2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

5/2x-(-2x+9/2x+2)-2=0

We get rid of parentheses

5/2x+2x-9/2x-2-2=0

We multiply all the terms by the denominator


2x*2x-2*2x-2*2x+5-9=0

We add all the numbers together, and all the variables

2x*2x-2*2x-2*2x-4=0

Wy multiply elements

4x^2-4x-4x-4=0

We add all the numbers together, and all the variables

4x^2-8x-4=0

a = 4; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·4·(-4)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{2}}{2*4}=\frac{8-8\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{2}}{2*4}=\frac{8+8\sqrt{2}}{8}
$