13-3/2x=37-x

Solution for 13-3/2x=37-x equation:

13-3/2x=37-x

We move all terms to the left:

13-3/2x-(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

-3/2x-(-1x+37)+13=0

We get rid of parentheses

-3/2x+1x-37+13=0

We multiply all the terms by the denominator


1x*2x-37*2x+13*2x-3=0

Wy multiply elements

2x^2-74x+26x-3=0

We add all the numbers together, and all the variables

2x^2-48x-3=0

a = 2; b = -48; c = -3;
Δ = b2-4ac
Δ = -482-4·2·(-3)
Δ = 2328
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:

$\sqrt{\Delta}=\sqrt{2328}=\sqrt{4*582}=\sqrt{4}*\sqrt{582}=2\sqrt{582}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{582}}{2*2}=\frac{48-2\sqrt{582}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{582}}{2*2}=\frac{48+2\sqrt{582}}{4}
$