100=x+2x+1/4x+1

Solution for 100=x+2x+1/4x+1 equation:

100=x+2x+1/4x+1

We move all terms to the left:

100-(x+2x+1/4x+1)=0


Domain of the equation: 4x+1)!=0

x∈R


We add all the numbers together, and all the variables

-(3x+1/4x+1)+100=0

We get rid of parentheses

-3x-1/4x-1+100=0

We multiply all the terms by the denominator


-3x*4x-1*4x+100*4x-1=0

Wy multiply elements

-12x^2-4x+400x-1=0

We add all the numbers together, and all the variables

-12x^2+396x-1=0

a = -12; b = 396; c = -1;
Δ = b2-4ac
Δ = 3962-4·(-12)·(-1)
Δ = 156768
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:

$\sqrt{\Delta}=\sqrt{156768}=\sqrt{16*9798}=\sqrt{16}*\sqrt{9798}=4\sqrt{9798}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(396)-4\sqrt{9798}}{2*-12}=\frac{-396-4\sqrt{9798}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(396)+4\sqrt{9798}}{2*-12}=\frac{-396+4\sqrt{9798}}{-24}
$