35-x=x+1/4x

Solution for 35-x=x+1/4x equation:

35-x=x+1/4x

We move all terms to the left:

35-x-(x+1/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-(+x+1/4x)+35=0

We add all the numbers together, and all the variables

-1x-(+x+1/4x)+35=0

We get rid of parentheses

-1x-x-1/4x+35=0

We multiply all the terms by the denominator


-1x*4x-x*4x+35*4x-1=0

Wy multiply elements

-4x^2-4x^2+140x-1=0

We add all the numbers together, and all the variables

-8x^2+140x-1=0

a = -8; b = 140; c = -1;
Δ = b2-4ac
Δ = 1402-4·(-8)·(-1)
Δ = 19568
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:

$\sqrt{\Delta}=\sqrt{19568}=\sqrt{16*1223}=\sqrt{16}*\sqrt{1223}=4\sqrt{1223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-4\sqrt{1223}}{2*-8}=\frac{-140-4\sqrt{1223}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+4\sqrt{1223}}{2*-8}=\frac{-140+4\sqrt{1223}}{-16}
$