5-x=1/2x+

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

5-x=1/2x+

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -2; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·(-2)·(-1)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{23}}{2*-2}=\frac{-10-2\sqrt{23}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{23}}{2*-2}=\frac{-10+2\sqrt{23}}{-4}
$