2=x-5/7x

Solution for 2=x-5/7x equation:

2=x-5/7x

We move all terms to the left:

2-(x-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

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

We get rid of parentheses

-x+5/7x+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

-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}
$