1/3(2x-1)=1/7(11-8x)

Solution for 1/3(2x-1)=1/7(11-8x) equation:

1/3(2x-1)=1/7(11-8x)

We move all terms to the left:

1/3(2x-1)-(1/7(11-8x))=0


Domain of the equation: 3(2x-1)!=0

x∈R



Domain of the equation: 7(11-8x))!=0

x∈R


We add all the numbers together, and all the variables

1/3(2x-1)-(1/7(-8x+11))=0

We calculate fractions


(7x(-)/(3(2x-1)*7(-8x+11)))+(-3x2/(3(2x-1)*7(-8x+11)))=0


We calculate terms in parentheses: +(7x(-)/(3(2x-1)*7(-8x+11))), so:

7x(-)/(3(2x-1)*7(-8x+11))

We add all the numbers together, and all the variables

7x0/(3(2x-1)*7(-8x+11))

We multiply all the terms by the denominator


7x0

We add all the numbers together, and all the variables

7x

Back to the equation:

+(7x)



We calculate terms in parentheses: +(-3x2/(3(2x-1)*7(-8x+11))), so:

-3x2/(3(2x-1)*7(-8x+11))

We multiply all the terms by the denominator


-3x2

We add all the numbers together, and all the variables

-3x^2

Back to the equation:

+(-3x^2)


We get rid of parentheses

-3x^2+7x=0

a = -3; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-3)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-3}=\frac{-14}{-6}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-3}=\frac{0}{-6}
=0
$