15-2x-x^2/x-4=0

Solution for 15-2x-x^2/x-4=0 equation:

15-2x-x^2/x-4=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-x^2/x-2x+11=0

We multiply all the terms by the denominator


-x^2-2x*x+11*x=0

We add all the numbers together, and all the variables

-1x^2+11x-2x*x=0

Wy multiply elements

-1x^2-2x^2+11x=0

We add all the numbers together, and all the variables

-3x^2+11x=0

a = -3; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-3)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-3}=\frac{-22}{-6}
=3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-3}=\frac{0}{-6}
=0
$