1/2x+2=0.5x+5

Solution for 1/2x+2=0.5x+5 equation:

1/2x+2=0.5x+5

We move all terms to the left:

1/2x+2-(0.5x+5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-0.5x-5+2=0

We multiply all the terms by the denominator


-(0.5x)*2x-5*2x+2*2x+1=0

We add all the numbers together, and all the variables

-(+0.5x)*2x-5*2x+2*2x+1=0

We multiply parentheses

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

Wy multiply elements

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

We add all the numbers together, and all the variables

-1x^2-6x+1=0

a = -1; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·(-1)·1
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{10}}{2*-1}=\frac{6-2\sqrt{10}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{10}}{2*-1}=\frac{6+2\sqrt{10}}{-2}
$