X+x+1/4x=100

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

X+X+1/4X=100

We move all terms to the left:

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


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We add all the numbers together, and all the variables

2X+1/4X-100=0

We multiply all the terms by the denominator


2X*4X-100*4X+1=0

Wy multiply elements

8X^2-400X+1=0

a = 8; b = -400; c = +1;
Δ = b2-4ac
Δ = -4002-4·8·1
Δ = 159968
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:

$\sqrt{\Delta}=\sqrt{159968}=\sqrt{16*9998}=\sqrt{16}*\sqrt{9998}=4\sqrt{9998}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-4\sqrt{9998}}{2*8}=\frac{400-4\sqrt{9998}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+4\sqrt{9998}}{2*8}=\frac{400+4\sqrt{9998}}{16}
$