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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


150x^2/100x^2+50x/100x^2+(-60x)/100x^2=0

We multiply all the terms by the denominator


150x^2+50x+(-60x)=0

We get rid of parentheses

150x^2+50x-60x=0

We add all the numbers together, and all the variables

150x^2-10x=0

a = 150; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·150·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*150}=\frac{0}{300}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*150}=\frac{20}{300}
=1/15
$