3/5(15x+20)=1/3(27x+36)

Solution for 3/5(15x+20)=1/3(27x+36) equation:

3/5(15x+20)=1/3(27x+36)

We move all terms to the left:

3/5(15x+20)-(1/3(27x+36))=0


Domain of the equation: 5(15x+20)!=0

x∈R



Domain of the equation: 3(27x+36))!=0

x∈R


We calculate fractions


(9x2/(5(15x+20)*3(27x+36)))+(-5x1/(5(15x+20)*3(27x+36)))=0


We calculate terms in parentheses: +(9x2/(5(15x+20)*3(27x+36))), so:

9x2/(5(15x+20)*3(27x+36))

We multiply all the terms by the denominator


9x2

We add all the numbers together, and all the variables

9x^2

Back to the equation:

+(9x^2)



We calculate terms in parentheses: +(-5x1/(5(15x+20)*3(27x+36))), so:

-5x1/(5(15x+20)*3(27x+36))

We multiply all the terms by the denominator


-5x1

We add all the numbers together, and all the variables

-5x

Back to the equation:

+(-5x)


We get rid of parentheses

9x^2-5x=0

a = 9; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·9·0
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*9}=\frac{0}{18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*9}=\frac{10}{18}
=5/9
$