3x-15/x=53

Solution for 3x-15/x=53 equation:

3x-15/x=53

We move all terms to the left:

3x-15/x-(53)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


3x*x-53*x-15=0

We add all the numbers together, and all the variables

-53x+3x*x-15=0

Wy multiply elements

3x^2-53x-15=0

a = 3; b = -53; c = -15;
Δ = b2-4ac
Δ = -532-4·3·(-15)
Δ = 2989
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:

$\sqrt{\Delta}=\sqrt{2989}=\sqrt{49*61}=\sqrt{49}*\sqrt{61}=7\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-7\sqrt{61}}{2*3}=\frac{53-7\sqrt{61}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+7\sqrt{61}}{2*3}=\frac{53+7\sqrt{61}}{6}
$