35-x=5+1/5x

Solution for 35-x=5+1/5x equation:

35-x=5+1/5x

We move all terms to the left:

35-x-(5+1/5x)=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-(1/5x+5)+35=0

We add all the numbers together, and all the variables

-1x-(1/5x+5)+35=0

We get rid of parentheses

-1x-1/5x-5+35=0

We multiply all the terms by the denominator


-1x*5x-5*5x+35*5x-1=0

Wy multiply elements

-5x^2-25x+175x-1=0

We add all the numbers together, and all the variables

-5x^2+150x-1=0

a = -5; b = 150; c = -1;
Δ = b2-4ac
Δ = 1502-4·(-5)·(-1)
Δ = 22480
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:

$\sqrt{\Delta}=\sqrt{22480}=\sqrt{16*1405}=\sqrt{16}*\sqrt{1405}=4\sqrt{1405}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-4\sqrt{1405}}{2*-5}=\frac{-150-4\sqrt{1405}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+4\sqrt{1405}}{2*-5}=\frac{-150+4\sqrt{1405}}{-10}
$