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 add all the numbers together, and all the variables

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

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 add all the numbers together, and all the variables

(-150x^2)+110x=0

We get rid of parentheses

-150x^2+110x=0

a = -150; b = 110; c = 0;
Δ = b2-4ac
Δ = 1102-4·(-150)·0
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-110}{2*-150}=\frac{-220}{-300}
=11/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+110}{2*-150}=\frac{0}{-300}
=0
$