1x*3-4/x=33/x

Solution for 1x*3-4/x=33/x equation:

1x*3-4/x=33/x

We move all terms to the left:

1x*3-4/x-(33/x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1x*3-4/x-(+33/x)=0

Wy multiply elements

3x-4/x-(+33/x)=0

We get rid of parentheses

3x-4/x-33/x=0

We multiply all the terms by the denominator


3x*x-4-33=0

We add all the numbers together, and all the variables

3x*x-37=0

Wy multiply elements

3x^2-37=0

a = 3; b = 0; c = -37;
Δ = b2-4ac
Δ = 02-4·3·(-37)
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{111}}{2*3}=\frac{0-2\sqrt{111}}{6}
=-\frac{2\sqrt{111}}{6}
=-\frac{\sqrt{111}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{111}}{2*3}=\frac{0+2\sqrt{111}}{6}
=\frac{2\sqrt{111}}{6}
=\frac{\sqrt{111}}{3}
$