X+x+1+1/4x=100

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

X+X+1+1/4X=100

We move all terms to the left:

X+X+1+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-99=0

We multiply all the terms by the denominator


2X*4X-99*4X+1=0

Wy multiply elements

8X^2-396X+1=0

a = 8; b = -396; c = +1;
Δ = b2-4ac
Δ = -3962-4·8·1
Δ = 156784
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:

$\sqrt{\Delta}=\sqrt{156784}=\sqrt{16*9799}=\sqrt{16}*\sqrt{9799}=4\sqrt{9799}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-396)-4\sqrt{9799}}{2*8}=\frac{396-4\sqrt{9799}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-396)+4\sqrt{9799}}{2*8}=\frac{396+4\sqrt{9799}}{16}
$