2/5x-7/10x+3/10=12

Solution for 2/5x-7/10x+3/10=12 equation:

2/5x-7/10x+3/10=12

We move all terms to the left:

2/5x-7/10x+3/10-(12)=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


determiningTheFunctionDomain
2/5x-7/10x-12+3/10=0

We calculate fractions


200x/500x^2+(-35x)/500x^2+15x/500x^2-12=0

We multiply all the terms by the denominator


200x+(-35x)+15x-12*500x^2=0

We add all the numbers together, and all the variables

215x+(-35x)-12*500x^2=0

Wy multiply elements

-6000x^2+215x+(-35x)=0

We get rid of parentheses

-6000x^2+215x-35x=0

We add all the numbers together, and all the variables

-6000x^2+180x=0

a = -6000; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·(-6000)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*-6000}=\frac{-360}{-12000}
=3/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*-6000}=\frac{0}{-12000}
=0
$