X=4n-3/2n

Solution for X=4n-3/2n equation:

X=4X-3/2X

We move all terms to the left:

X-(4X-3/2X)=0


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+4X-3/2X)=0

We get rid of parentheses

X-4X+3/2X=0

We multiply all the terms by the denominator


X*2X-4X*2X+3=0

Wy multiply elements

2X^2-8X^2+3=0

We add all the numbers together, and all the variables

-6X^2+3=0

a = -6; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-6)·3
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*-6}=\frac{0-6\sqrt{2}}{-12}
=-\frac{6\sqrt{2}}{-12}
=-\frac{\sqrt{2}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*-6}=\frac{0+6\sqrt{2}}{-12}
=\frac{6\sqrt{2}}{-12}
=\frac{\sqrt{2}}{-2}
$