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

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

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

We move all terms to the left:

-3/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

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

12x^2-1x=0

a = 12; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·12·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*12}=\frac{2}{24}
=1/12
$