44+x=3/7x

Solution for 44+x=3/7x equation:

44+x=3/7x

We move all terms to the left:

44+x-(3/7x)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+3/7x)+44=0

We get rid of parentheses

x-3/7x+44=0

We multiply all the terms by the denominator


x*7x+44*7x-3=0

Wy multiply elements

7x^2+308x-3=0

a = 7; b = 308; c = -3;
Δ = b2-4ac
Δ = 3082-4·7·(-3)
Δ = 94948
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:

$\sqrt{\Delta}=\sqrt{94948}=\sqrt{4*23737}=\sqrt{4}*\sqrt{23737}=2\sqrt{23737}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(308)-2\sqrt{23737}}{2*7}=\frac{-308-2\sqrt{23737}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(308)+2\sqrt{23737}}{2*7}=\frac{-308+2\sqrt{23737}}{14}
$