9/5x+3/2x=-33/10

Solution for 9/5x+3/2x=-33/10 equation:

9/5x+3/2x=-33/10

We move all terms to the left:

9/5x+3/2x-(-33/10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

9/5x+3/2x+33/10=0

We calculate fractions


660x^2/100x^2+180x/100x^2+150x/100x^2=0

We multiply all the terms by the denominator


660x^2+180x+150x=0

We add all the numbers together, and all the variables

660x^2+330x=0

a = 660; b = 330; c = 0;
Δ = b2-4ac
Δ = 3302-4·660·0
Δ = 108900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{108900}=330$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(330)-330}{2*660}=\frac{-660}{1320}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(330)+330}{2*660}=\frac{0}{1320}
=0
$