100-x=1/4*x

Solution for 100-x=1/4*x equation:

100-x=1/4x

We move all terms to the left:

100-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-(+1/4x)+100=0

We add all the numbers together, and all the variables

-1x-(+1/4x)+100=0

We get rid of parentheses

-1x-1/4x+100=0

We multiply all the terms by the denominator


-1x*4x+100*4x-1=0

Wy multiply elements

-4x^2+400x-1=0

a = -4; b = 400; c = -1;
Δ = b2-4ac
Δ = 4002-4·(-4)·(-1)
Δ = 159984
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:

$\sqrt{\Delta}=\sqrt{159984}=\sqrt{144*1111}=\sqrt{144}*\sqrt{1111}=12\sqrt{1111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-12\sqrt{1111}}{2*-4}=\frac{-400-12\sqrt{1111}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+12\sqrt{1111}}{2*-4}=\frac{-400+12\sqrt{1111}}{-8}
$