6+2x=5/7x

Solution for 6+2x=5/7x equation:

6+2x=5/7x

We move all terms to the left:

6+2x-(5/7x)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+5/7x)+6=0

We get rid of parentheses

2x-5/7x+6=0

We multiply all the terms by the denominator


2x*7x+6*7x-5=0

Wy multiply elements

14x^2+42x-5=0

a = 14; b = 42; c = -5;
Δ = b2-4ac
Δ = 422-4·14·(-5)
Δ = 2044
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:

$\sqrt{\Delta}=\sqrt{2044}=\sqrt{4*511}=\sqrt{4}*\sqrt{511}=2\sqrt{511}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{511}}{2*14}=\frac{-42-2\sqrt{511}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{511}}{2*14}=\frac{-42+2\sqrt{511}}{28}
$