3/2x+12/5x=13/20

Solution for 3/2x+12/5x=13/20 equation:

3/2x+12/5x=13/20

We move all terms to the left:

3/2x+12/5x-(13/20)=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

3/2x+12/5x-(+13/20)=0

We get rid of parentheses

3/2x+12/5x-13/20=0

We calculate fractions


(-650x^2)/400x^2+600x/400x^2+960x/400x^2=0

We multiply all the terms by the denominator


(-650x^2)+600x+960x=0

We add all the numbers together, and all the variables

(-650x^2)+1560x=0

We get rid of parentheses

-650x^2+1560x=0

a = -650; b = 1560; c = 0;
Δ = b2-4ac
Δ = 15602-4·(-650)·0
Δ = 2433600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2433600}=1560$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1560)-1560}{2*-650}=\frac{-3120}{-1300}
=2+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1560)+1560}{2*-650}=\frac{0}{-1300}
=0
$