3x-3/x=146

Solution for 3x-3/x=146 equation:

3x-3/x=146

We move all terms to the left:

3x-3/x-(146)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


3x*x-146*x-3=0

We add all the numbers together, and all the variables

-146x+3x*x-3=0

Wy multiply elements

3x^2-146x-3=0

a = 3; b = -146; c = -3;
Δ = b2-4ac
Δ = -1462-4·3·(-3)
Δ = 21352
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:

$\sqrt{\Delta}=\sqrt{21352}=\sqrt{4*5338}=\sqrt{4}*\sqrt{5338}=2\sqrt{5338}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-146)-2\sqrt{5338}}{2*3}=\frac{146-2\sqrt{5338}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-146)+2\sqrt{5338}}{2*3}=\frac{146+2\sqrt{5338}}{6}
$