1/5x+3/10x=-3/2

Solution for 1/5x+3/10x=-3/2 equation:

1/5x+3/10x=-3/2

We move all terms to the left:

1/5x+3/10x-(-3/2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We get rid of parentheses

1/5x+3/10x+3/2=0

We calculate fractions


150x^2/200x^2+40x/200x^2+60x/200x^2=0

We multiply all the terms by the denominator


150x^2+40x+60x=0

We add all the numbers together, and all the variables

150x^2+100x=0

a = 150; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·150·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100}{2*150}=\frac{-200}{300}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*150}=\frac{0}{300}
=0
$