3/x-2=15x

Solution for 3/x-2=15x equation:

3/x-2=15x

We move all terms to the left:

3/x-2-(15x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-15x+3/x-2=0

We multiply all the terms by the denominator


-15x*x-2*x+3=0

We add all the numbers together, and all the variables

-2x-15x*x+3=0

Wy multiply elements

-15x^2-2x+3=0

a = -15; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-15)·3
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{46}}{2*-15}=\frac{2-2\sqrt{46}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{46}}{2*-15}=\frac{2+2\sqrt{46}}{-30}
$