x+13=1/2x+16

Solution for x+13=1/2x+16 equation:

x+13=1/2x+16

We move all terms to the left:

x+13-(1/2x+16)=0


Domain of the equation: 2x+16)!=0

x∈R


We get rid of parentheses

x-1/2x-16+13=0

We multiply all the terms by the denominator


x*2x-16*2x+13*2x-1=0

Wy multiply elements

2x^2-32x+26x-1=0

We add all the numbers together, and all the variables

2x^2-6x-1=0

a = 2; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·2·(-1)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{11}}{2*2}=\frac{6-2\sqrt{11}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{11}}{2*2}=\frac{6+2\sqrt{11}}{4}
$