11/4x=26+x

Solution for 11/4x=26+x equation:

11/4x=26+x

We move all terms to the left:

11/4x-(26+x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

11/4x-(x+26)=0

We get rid of parentheses

11/4x-x-26=0

We multiply all the terms by the denominator


-x*4x-26*4x+11=0

Wy multiply elements

-4x^2-104x+11=0

a = -4; b = -104; c = +11;
Δ = b2-4ac
Δ = -1042-4·(-4)·11
Δ = 10992
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:

$\sqrt{\Delta}=\sqrt{10992}=\sqrt{16*687}=\sqrt{16}*\sqrt{687}=4\sqrt{687}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-4\sqrt{687}}{2*-4}=\frac{104-4\sqrt{687}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+4\sqrt{687}}{2*-4}=\frac{104+4\sqrt{687}}{-8}
$