-4/6x+10=-2/12x+20

Solution for -4/6x+10=-2/12x+20 equation:

-4/6x+10=-2/12x+20

We move all terms to the left:

-4/6x+10-(-2/12x+20)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 12x+20)!=0

x∈R


We get rid of parentheses

-4/6x+2/12x-20+10=0

We calculate fractions


(-48x)/72x^2+12x/72x^2-20+10=0

We add all the numbers together, and all the variables

(-48x)/72x^2+12x/72x^2-10=0

We multiply all the terms by the denominator


(-48x)+12x-10*72x^2=0

We add all the numbers together, and all the variables

12x+(-48x)-10*72x^2=0

Wy multiply elements

-720x^2+12x+(-48x)=0

We get rid of parentheses

-720x^2+12x-48x=0

We add all the numbers together, and all the variables

-720x^2-36x=0

a = -720; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·(-720)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*-720}=\frac{0}{-1440}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*-720}=\frac{72}{-1440}
=-1/20
$