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

Solution for 2x+5=x-2+1/2x equation:

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

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-2x^2+4x+10x-1=0

We add all the numbers together, and all the variables

2x^2+14x-1=0

a = 2; b = 14; c = -1;
Δ = b2-4ac
Δ = 142-4·2·(-1)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{51}}{2*2}=\frac{-14-2\sqrt{51}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{51}}{2*2}=\frac{-14+2\sqrt{51}}{4}
$