7+3/7x=2x

Solution for 7+3/7x=2x equation:

7+3/7x=2x

We move all terms to the left:

7+3/7x-(2x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+3/7x+7=0

We multiply all the terms by the denominator


-2x*7x+7*7x+3=0

Wy multiply elements

-14x^2+49x+3=0

a = -14; b = 49; c = +3;
Δ = b2-4ac
Δ = 492-4·(-14)·3
Δ = 2569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-\sqrt{2569}}{2*-14}=\frac{-49-\sqrt{2569}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+\sqrt{2569}}{2*-14}=\frac{-49+\sqrt{2569}}{-28}
$