2x+30/x=-17

Solution for 2x+30/x=-17 equation:

2x+30/x=-17

We move all terms to the left:

2x+30/x-(-17)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x+30/x+17=0

We multiply all the terms by the denominator


2x*x+17*x+30=0

We add all the numbers together, and all the variables

17x+2x*x+30=0

Wy multiply elements

2x^2+17x+30=0

a = 2; b = 17; c = +30;
Δ = b2-4ac
Δ = 172-4·2·30
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-7}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+7}{2*2}=\frac{-10}{4}
=-2+1/2
$