(5/7)x=3/7+x

Solution for (5/7)x=3/7+x equation:

(5/7)x=3/7+x

We move all terms to the left:

(5/7)x-(3/7+x)=0


Domain of the equation: 7)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 7+x)!=0

We move all terms containing x to the left, all other terms to the right

x)!=-7

x!=-7/1

x!=-7

x∈R


We add all the numbers together, and all the variables

(+5/7)x-(+x+3/7)=0

We multiply parentheses

5x^2-(+x+3/7)=0

We get rid of parentheses

5x^2-x-3/7=0

We multiply all the terms by the denominator


5x^2*7-x*7-3=0

Wy multiply elements

35x^2-7x-3=0

a = 35; b = -7; c = -3;
Δ = b2-4ac
Δ = -72-4·35·(-3)
Δ = 469
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{-(-7)-\sqrt{469}}{2*35}=\frac{7-\sqrt{469}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{469}}{2*35}=\frac{7+\sqrt{469}}{70}
$