3/4(16x-20)=1/3(27x+18)

Solution for 3/4(16x-20)=1/3(27x+18) equation:

3/4(16x-20)=1/3(27x+18)

We move all terms to the left:

3/4(16x-20)-(1/3(27x+18))=0


Domain of the equation: 4(16x-20)!=0

x∈R



Domain of the equation: 3(27x+18))!=0

x∈R


We calculate fractions


(9x2/(4(16x-20)*3(27x+18)))+(-4x1/(4(16x-20)*3(27x+18)))=0


We calculate terms in parentheses: +(9x2/(4(16x-20)*3(27x+18))), so:

9x2/(4(16x-20)*3(27x+18))

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: +(-4x1/(4(16x-20)*3(27x+18))), so:

-4x1/(4(16x-20)*3(27x+18))

We multiply all the terms by the denominator


-4x1

We add all the numbers together, and all the variables

-4x

Back to the equation:

+(-4x)


We get rid of parentheses

9x^2-4x=0

a = 9; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·9·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*9}=\frac{0}{18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*9}=\frac{8}{18}
=4/9
$