3+x=8/7x

Solution for 3+x=8/7x equation:

3+x=8/7x

We move all terms to the left:

3+x-(8/7x)=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-(+8/7x)+3=0

We get rid of parentheses

x-8/7x+3=0

We multiply all the terms by the denominator


x*7x+3*7x-8=0

Wy multiply elements

7x^2+21x-8=0

a = 7; b = 21; c = -8;
Δ = b2-4ac
Δ = 212-4·7·(-8)
Δ = 665
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{-(21)-\sqrt{665}}{2*7}=\frac{-21-\sqrt{665}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{665}}{2*7}=\frac{-21+\sqrt{665}}{14}
$