330x=3/4x

Solution for 330x=3/4x equation:

330x=3/4x

We move all terms to the left:

330x-(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

330x-(+3/4x)=0

We get rid of parentheses

330x-3/4x=0

We multiply all the terms by the denominator


330x*4x-3=0

Wy multiply elements

1320x^2-3=0

a = 1320; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·1320·(-3)
Δ = 15840
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:

$\sqrt{\Delta}=\sqrt{15840}=\sqrt{144*110}=\sqrt{144}*\sqrt{110}=12\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{110}}{2*1320}=\frac{0-12\sqrt{110}}{2640}
=-\frac{12\sqrt{110}}{2640}
=-\frac{\sqrt{110}}{220}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{110}}{2*1320}=\frac{0+12\sqrt{110}}{2640}
=\frac{12\sqrt{110}}{2640}
=\frac{\sqrt{110}}{220}
$