3+5/7x=1+x

Solution for 3+5/7x=1+x equation:

3+5/7x=1+x

We move all terms to the left:

3+5/7x-(1+x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

5/7x-(x+1)+3=0

We get rid of parentheses

5/7x-x-1+3=0

We multiply all the terms by the denominator


-x*7x-1*7x+3*7x+5=0

Wy multiply elements

-7x^2-7x+21x+5=0

We add all the numbers together, and all the variables

-7x^2+14x+5=0

a = -7; b = 14; c = +5;
Δ = b2-4ac
Δ = 142-4·(-7)·5
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{21}}{2*-7}=\frac{-14-4\sqrt{21}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{21}}{2*-7}=\frac{-14+4\sqrt{21}}{-14}
$