x=50+5/7x

Solution for x=50+5/7x equation:

x=50+5/7x

We move all terms to the left:

x-(50+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+50)=0

We get rid of parentheses

x-5/7x-50=0

We multiply all the terms by the denominator


x*7x-50*7x-5=0

Wy multiply elements

7x^2-350x-5=0

a = 7; b = -350; c = -5;
Δ = b2-4ac
Δ = -3502-4·7·(-5)
Δ = 122640
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:

$\sqrt{\Delta}=\sqrt{122640}=\sqrt{16*7665}=\sqrt{16}*\sqrt{7665}=4\sqrt{7665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-4\sqrt{7665}}{2*7}=\frac{350-4\sqrt{7665}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+4\sqrt{7665}}{2*7}=\frac{350+4\sqrt{7665}}{14}
$