5-x=1/2x+3

Solution for 5-x=1/2x+3 equation:

5-x=1/2x+3

We move all terms to the left:

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


Domain of the equation: 2x+3)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-2x^2-6x+10x-1=0

We add all the numbers together, and all the variables

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

a = -2; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·(-2)·(-1)
Δ = 8
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:

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