3/10x+12=2/5x-28

Solution for 3/10x+12=2/5x-28 equation:

3/10x+12=2/5x-28

We move all terms to the left:

3/10x+12-(2/5x-28)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x-28)!=0

x∈R


We get rid of parentheses

3/10x-2/5x+28+12=0

We calculate fractions


15x/50x^2+(-20x)/50x^2+28+12=0

We add all the numbers together, and all the variables

15x/50x^2+(-20x)/50x^2+40=0

We multiply all the terms by the denominator


15x+(-20x)+40*50x^2=0

Wy multiply elements

2000x^2+15x+(-20x)=0

We get rid of parentheses

2000x^2+15x-20x=0

We add all the numbers together, and all the variables

2000x^2-5x=0

a = 2000; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·2000·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*2000}=\frac{0}{4000}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*2000}=\frac{10}{4000}
=1/400
$