1/3(2x+7)=1/6(4-x)

Solution for 1/3(2x+7)=1/6(4-x) equation:

1/3(2x+7)=1/6(4-x)

We move all terms to the left:

1/3(2x+7)-(1/6(4-x))=0


Domain of the equation: 3(2x+7)!=0

x∈R



Domain of the equation: 6(4-x))!=0

x∈R


We add all the numbers together, and all the variables

1/3(2x+7)-(1/6(-1x+4))=0

We calculate fractions


(6x(-)/(3(2x+7)*6(-1x+4)))+(-3x2/(3(2x+7)*6(-1x+4)))=0


We calculate terms in parentheses: +(6x(-)/(3(2x+7)*6(-1x+4))), so:

6x(-)/(3(2x+7)*6(-1x+4))

We add all the numbers together, and all the variables

6x0/(3(2x+7)*6(-1x+4))

We multiply all the terms by the denominator


6x0

We add all the numbers together, and all the variables

6x

Back to the equation:

+(6x)



We calculate terms in parentheses: +(-3x2/(3(2x+7)*6(-1x+4))), so:

-3x2/(3(2x+7)*6(-1x+4))

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+6x=0

a = -3; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-3)·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*-3}=\frac{-12}{-6}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-3}=\frac{0}{-6}
=0
$