x^2/x+3-2x/x+3-15/x+3=-8

Solution for x^2/x+3-2x/x+3-15/x+3=-8 equation:

x^2/x+3-2x/x+3-15/x+3=-8

We move all terms to the left:

x^2/x+3-2x/x+3-15/x+3-(-8)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x^2/x-2x/x-15/x+17=0

We multiply all the terms by the denominator


x^2-2x+17*x-15=0

We add all the numbers together, and all the variables

x^2+15x-15=0

a = 1; b = 15; c = -15;
Δ = b2-4ac
Δ = 152-4·1·(-15)
Δ = 285
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{285}}{2*1}=\frac{-15-\sqrt{285}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{285}}{2*1}=\frac{-15+\sqrt{285}}{2}
$