4x=11/2x=3

Solution for 4x=11/2x=3 equation:

4x=11/2x=3

We move all terms to the left:

4x-(11/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+11/2x)=0

We get rid of parentheses

4x-11/2x=0

We multiply all the terms by the denominator


4x*2x-11=0

Wy multiply elements

8x^2-11=0

a = 8; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·8·(-11)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{22}}{2*8}=\frac{0-4\sqrt{22}}{16}
=-\frac{4\sqrt{22}}{16}
=-\frac{\sqrt{22}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{22}}{2*8}=\frac{0+4\sqrt{22}}{16}
=\frac{4\sqrt{22}}{16}
=\frac{\sqrt{22}}{4}
$