1/6(12x-30)=1/5(25x+20)

Solution for 1/6(12x-30)=1/5(25x+20) equation:

1/6(12x-30)=1/5(25x+20)

We move all terms to the left:

1/6(12x-30)-(1/5(25x+20))=0


Domain of the equation: 6(12x-30)!=0

x∈R



Domain of the equation: 5(25x+20))!=0

x∈R


We calculate fractions


(5x2/(6(12x-30)*5(25x+20)))+(-6x1/(6(12x-30)*5(25x+20)))=0


We calculate terms in parentheses: +(5x2/(6(12x-30)*5(25x+20))), so:

5x2/(6(12x-30)*5(25x+20))

We multiply all the terms by the denominator


5x2

We add all the numbers together, and all the variables

5x^2

Back to the equation:

+(5x^2)



We calculate terms in parentheses: +(-6x1/(6(12x-30)*5(25x+20))), so:

-6x1/(6(12x-30)*5(25x+20))

We multiply all the terms by the denominator


-6x1

We add all the numbers together, and all the variables

-6x

Back to the equation:

+(-6x)


We get rid of parentheses

5x^2-6x=0

a = 5; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·5·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*5}=\frac{12}{10}
=1+1/5
$