3x-15=2/x+5

Solution for 3x-15=2/x+5 equation:

3x-15=2/x+5

We move all terms to the left:

3x-15-(2/x+5)=0


Domain of the equation: x+5)!=0

x∈R


We get rid of parentheses

3x-2/x-5-15=0

We multiply all the terms by the denominator


3x*x-5*x-15*x-2=0

We add all the numbers together, and all the variables

-20x+3x*x-2=0

Wy multiply elements

3x^2-20x-2=0

a = 3; b = -20; c = -2;
Δ = b2-4ac
Δ = -202-4·3·(-2)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{106}}{2*3}=\frac{20-2\sqrt{106}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{106}}{2*3}=\frac{20+2\sqrt{106}}{6}
$