x=35+3/5x

Solution for x=35+3/5x equation:

x=35+3/5x

We move all terms to the left:

x-(35+3/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(3/5x+35)=0

We get rid of parentheses

x-3/5x-35=0

We multiply all the terms by the denominator


x*5x-35*5x-3=0

Wy multiply elements

5x^2-175x-3=0

a = 5; b = -175; c = -3;
Δ = b2-4ac
Δ = -1752-4·5·(-3)
Δ = 30685
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:

$\sqrt{\Delta}=\sqrt{30685}=\sqrt{361*85}=\sqrt{361}*\sqrt{85}=19\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-175)-19\sqrt{85}}{2*5}=\frac{175-19\sqrt{85}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-175)+19\sqrt{85}}{2*5}=\frac{175+19\sqrt{85}}{10}
$