-3x/x+5/2x=-6

Solution for -3x/x+5/2x=-6 equation:

-3x/x+5/2x=-6

We move all terms to the left:

-3x/x+5/2x-(-6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-3x/x+5/2x+6=0

We calculate fractions


(-6x^2)/2x^2+5x/2x^2+6=0

We multiply all the terms by the denominator


(-6x^2)+5x+6*2x^2=0

Wy multiply elements

(-6x^2)+12x^2+5x=0

We get rid of parentheses

-6x^2+12x^2+5x=0

We add all the numbers together, and all the variables

6x^2+5x=0

a = 6; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·6·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*6}=\frac{-10}{12}
=-5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*6}=\frac{0}{12}
=0
$