1/2(16x+8)-5=-1/3(24x-9)

Solution for 1/2(16x+8)-5=-1/3(24x-9) equation:

1/2(16x+8)-5=-1/3(24x-9)

We move all terms to the left:

1/2(16x+8)-5-(-1/3(24x-9))=0


Domain of the equation: 2(16x+8)!=0

x∈R



Domain of the equation: 3(24x-9))!=0

x∈R


We calculate fractions


(3x2/(2(16x+8)*3(24x-9)))+(-(-2x1)/(2(16x+8)*3(24x-9)))-5=0


We calculate terms in parentheses: +(3x2/(2(16x+8)*3(24x-9))), so:

3x2/(2(16x+8)*3(24x-9))

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 calculate terms in parentheses: +(-(-2x1)/(2(16x+8)*3(24x-9))), so:

-(-2x1)/(2(16x+8)*3(24x-9))

We add all the numbers together, and all the variables

-(-2x)/(2(16x+8)*3(24x-9))

We multiply all the terms by the denominator


-(-2x)

We get rid of parentheses

2x

Back to the equation:

+(2x)


a = 3; b = 2; c = -5;
Δ = b2-4ac
Δ = 22-4·3·(-5)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8}{2*3}=\frac{-10}{6}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8}{2*3}=\frac{6}{6}
=1
$