13-1/2x=37-x

Solution for 13-1/2x=37-x equation:

13-1/2x=37-x

We move all terms to the left:

13-1/2x-(37-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-(-1x+37)+13=0

We get rid of parentheses

-1/2x+1x-37+13=0

We multiply all the terms by the denominator


1x*2x-37*2x+13*2x-1=0

Wy multiply elements

2x^2-74x+26x-1=0

We add all the numbers together, and all the variables

2x^2-48x-1=0

a = 2; b = -48; c = -1;
Δ = b2-4ac
Δ = -482-4·2·(-1)
Δ = 2312
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:

$\sqrt{\Delta}=\sqrt{2312}=\sqrt{1156*2}=\sqrt{1156}*\sqrt{2}=34\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-34\sqrt{2}}{2*2}=\frac{48-34\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+34\sqrt{2}}{2*2}=\frac{48+34\sqrt{2}}{4}
$