11/8x=4x

Solution for 11/8x=4x equation:

11/8x=4x

We move all terms to the left:

11/8x-(4x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+11/8x=0

We multiply all the terms by the denominator


-4x*8x+11=0

Wy multiply elements

-32x^2+11=0

a = -32; b = 0; c = +11;
Δ = b2-4ac
Δ = 02-4·(-32)·11
Δ = 1408
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:

$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{22}}{2*-32}=\frac{0-8\sqrt{22}}{-64}
=-\frac{8\sqrt{22}}{-64}
=-\frac{\sqrt{22}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{22}}{2*-32}=\frac{0+8\sqrt{22}}{-64}
=\frac{8\sqrt{22}}{-64}
=\frac{\sqrt{22}}{-8}
$