4.5x=3/4x

Solution for 4.5x=3/4x equation:

4.5x=3/4x

We move all terms to the left:

4.5x-(3/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4.5x-(+3/4x)=0

We get rid of parentheses

4.5x-3/4x=0

We multiply all the terms by the denominator


(4.5x)*4x-3=0

We add all the numbers together, and all the variables

(+4.5x)*4x-3=0

We multiply parentheses

16x^2-3=0

a = 16; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·16·(-3)
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{-(0)-8\sqrt{3}}{2*16}=\frac{0-8\sqrt{3}}{32}
=-\frac{8\sqrt{3}}{32}
=-\frac{\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*16}=\frac{0+8\sqrt{3}}{32}
=\frac{8\sqrt{3}}{32}
=\frac{\sqrt{3}}{4}
$