50+2/7x=x

Solution for 50+2/7x=x equation:

50+2/7x=x

We move all terms to the left:

50+2/7x-(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

-1x+2/7x+50=0

We multiply all the terms by the denominator


-1x*7x+50*7x+2=0

Wy multiply elements

-7x^2+350x+2=0

a = -7; b = 350; c = +2;
Δ = b2-4ac
Δ = 3502-4·(-7)·2
Δ = 122556
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:

$\sqrt{\Delta}=\sqrt{122556}=\sqrt{4*30639}=\sqrt{4}*\sqrt{30639}=2\sqrt{30639}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(350)-2\sqrt{30639}}{2*-7}=\frac{-350-2\sqrt{30639}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(350)+2\sqrt{30639}}{2*-7}=\frac{-350+2\sqrt{30639}}{-14}
$