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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We calculate fractions


(-30x)/20x^2+6x/20x^2-12=0

We multiply all the terms by the denominator


(-30x)+6x-12*20x^2=0

We add all the numbers together, and all the variables

6x+(-30x)-12*20x^2=0

Wy multiply elements

-240x^2+6x+(-30x)=0

We get rid of parentheses

-240x^2+6x-30x=0

We add all the numbers together, and all the variables

-240x^2-24x=0

a = -240; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·(-240)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*-240}=\frac{0}{-480}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*-240}=\frac{48}{-480}
=-1/10
$