2+x-(5+3/2x)=2x

Solution for 2+x-(5+3/2x)=2x equation:

2+x-(5+3/2x)=2x

We move all terms to the left:

2+x-(5+3/2x)-(2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(3/2x+5)-2x+2=0

We add all the numbers together, and all the variables

-1x-(3/2x+5)+2=0

We get rid of parentheses

-1x-3/2x-5+2=0

We multiply all the terms by the denominator


-1x*2x-5*2x+2*2x-3=0

Wy multiply elements

-2x^2-10x+4x-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 = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3}}{2*-2}=\frac{6-2\sqrt{3}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3}}{2*-2}=\frac{6+2\sqrt{3}}{-4}
$