x=42/3(2x)

Solution for x=42/3(2x) equation:

x=42/3(2x)

We move all terms to the left:

x-(42/3(2x))=0


Domain of the equation: 32x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+42/32x)=0

We get rid of parentheses

x-42/32x=0

We multiply all the terms by the denominator


x*32x-42=0

Wy multiply elements

32x^2-42=0

a = 32; b = 0; c = -42;
Δ = b2-4ac
Δ = 02-4·32·(-42)
Δ = 5376
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:

$\sqrt{\Delta}=\sqrt{5376}=\sqrt{256*21}=\sqrt{256}*\sqrt{21}=16\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{21}}{2*32}=\frac{0-16\sqrt{21}}{64}
=-\frac{16\sqrt{21}}{64}
=-\frac{\sqrt{21}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{21}}{2*32}=\frac{0+16\sqrt{21}}{64}
=\frac{16\sqrt{21}}{64}
=\frac{\sqrt{21}}{4}
$