11/4x=x+1

Solution for 11/4x=x+1 equation:

11/4x=x+1

We move all terms to the left:

11/4x-(x+1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

11/4x-x-1=0

We multiply all the terms by the denominator


-x*4x-1*4x+11=0

Wy multiply elements

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

a = -4; b = -4; c = +11;
Δ = b2-4ac
Δ = -42-4·(-4)·11
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{3}}{2*-4}=\frac{4-8\sqrt{3}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{3}}{2*-4}=\frac{4+8\sqrt{3}}{-8}
$