110=x+1/4x

Solution for 110=x+1/4x equation:

110=x+1/4x

We move all terms to the left:

110-(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)+110=0

We get rid of parentheses

-x-1/4x+110=0

We multiply all the terms by the denominator


-x*4x+110*4x-1=0

Wy multiply elements

-4x^2+440x-1=0

a = -4; b = 440; c = -1;
Δ = b2-4ac
Δ = 4402-4·(-4)·(-1)
Δ = 193584
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:

$\sqrt{\Delta}=\sqrt{193584}=\sqrt{16*12099}=\sqrt{16}*\sqrt{12099}=4\sqrt{12099}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(440)-4\sqrt{12099}}{2*-4}=\frac{-440-4\sqrt{12099}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(440)+4\sqrt{12099}}{2*-4}=\frac{-440+4\sqrt{12099}}{-8}
$