2/5x-12+3/10x=30

Solution for 2/5x-12+3/10x=30 equation:

2/5x-12+3/10x=30

We move all terms to the left:

2/5x-12+3/10x-(30)=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 add all the numbers together, and all the variables

2/5x+3/10x-42=0

We calculate fractions


20x/50x^2+15x/50x^2-42=0

We multiply all the terms by the denominator


20x+15x-42*50x^2=0

We add all the numbers together, and all the variables

35x-42*50x^2=0

Wy multiply elements

-2100x^2+35x=0

a = -2100; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·(-2100)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*-2100}=\frac{-70}{-4200}
=1/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*-2100}=\frac{0}{-4200}
=0
$