1/2x+3=16+x

Solution for 1/2x+3=16+x equation:

1/2x+3=16+x

We move all terms to the left:

1/2x+3-(16+x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(x+16)+3=0

We get rid of parentheses

1/2x-x-16+3=0

We multiply all the terms by the denominator


-x*2x-16*2x+3*2x+1=0

Wy multiply elements

-2x^2-32x+6x+1=0

We add all the numbers together, and all the variables

-2x^2-26x+1=0

a = -2; b = -26; c = +1;
Δ = b2-4ac
Δ = -262-4·(-2)·1
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-6\sqrt{19}}{2*-2}=\frac{26-6\sqrt{19}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+6\sqrt{19}}{2*-2}=\frac{26+6\sqrt{19}}{-4}
$