2/3(2x-3)=4/5(3-4x)

Solution for 2/3(2x-3)=4/5(3-4x) equation:

2/3(2x-3)=4/5(3-4x)

We move all terms to the left:

2/3(2x-3)-(4/5(3-4x))=0


Domain of the equation: 3(2x-3)!=0

x∈R



Domain of the equation: 5(3-4x))!=0

x∈R


We add all the numbers together, and all the variables

2/3(2x-3)-(4/5(-4x+3))=0

We calculate fractions


(10x(-)/(3(2x-3)*5(-4x+3)))+(-12x2/(3(2x-3)*5(-4x+3)))=0


We calculate terms in parentheses: +(10x(-)/(3(2x-3)*5(-4x+3))), so:

10x(-)/(3(2x-3)*5(-4x+3))

We add all the numbers together, and all the variables

10x0/(3(2x-3)*5(-4x+3))

We multiply all the terms by the denominator


10x0

We add all the numbers together, and all the variables

10x

Back to the equation:

+(10x)



We calculate terms in parentheses: +(-12x2/(3(2x-3)*5(-4x+3))), so:

-12x2/(3(2x-3)*5(-4x+3))

We multiply all the terms by the denominator


-12x2

We add all the numbers together, and all the variables

-12x^2

Back to the equation:

+(-12x^2)


We get rid of parentheses

-12x^2+10x=0

a = -12; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-12)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-12}=\frac{-20}{-24}
=5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-12}=\frac{0}{-24}
=0
$