1/9(4-7x)=1/2(8+2x)

Solution for 1/9(4-7x)=1/2(8+2x) equation:

1/9(4-7x)=1/2(8+2x)

We move all terms to the left:

1/9(4-7x)-(1/2(8+2x))=0


Domain of the equation: 9(4-7x)!=0

x∈R



Domain of the equation: 2(8+2x))!=0

x∈R


We add all the numbers together, and all the variables

1/9(-7x+4)-(1/2(2x+8))=0

We calculate fractions


(2x2/(9(-7x+4)*2(2x+8)))+(-9x0/(9(-7x+4)*2(2x+8)))=0


We calculate terms in parentheses: +(2x2/(9(-7x+4)*2(2x+8))), so:

2x2/(9(-7x+4)*2(2x+8))

We multiply all the terms by the denominator


2x2

We add all the numbers together, and all the variables

2x^2

Back to the equation:

+(2x^2)



We calculate terms in parentheses: +(-9x0/(9(-7x+4)*2(2x+8))), so:

-9x0/(9(-7x+4)*2(2x+8))

We multiply all the terms by the denominator


-9x0

We add all the numbers together, and all the variables

-9x

Back to the equation:

+(-9x)


We get rid of parentheses

2x^2-9x=0

a = 2; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·2·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*2}=\frac{18}{4}
=4+1/2
$