1/2(10x+16)-6=-2/3(21x-24)

Solution for 1/2(10x+16)-6=-2/3(21x-24) equation:

1/2(10x+16)-6=-2/3(21x-24)

We move all terms to the left:

1/2(10x+16)-6-(-2/3(21x-24))=0


Domain of the equation: 2(10x+16)!=0

x∈R



Domain of the equation: 3(21x-24))!=0

x∈R


We calculate fractions


(3x2/(2(10x+16)*3(21x-24)))+(-(-4x1)/(2(10x+16)*3(21x-24)))-6=0


We calculate terms in parentheses: +(3x2/(2(10x+16)*3(21x-24))), so:

3x2/(2(10x+16)*3(21x-24))

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: +(-(-4x1)/(2(10x+16)*3(21x-24))), so:

-(-4x1)/(2(10x+16)*3(21x-24))

We add all the numbers together, and all the variables

-(-4x)/(2(10x+16)*3(21x-24))

We multiply all the terms by the denominator


-(-4x)

We get rid of parentheses

4x

Back to the equation:

+(4x)


a = 3; b = 4; c = -6;
Δ = b2-4ac
Δ = 42-4·3·(-6)
Δ = 88
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{22}}{2*3}=\frac{-4-2\sqrt{22}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{22}}{2*3}=\frac{-4+2\sqrt{22}}{6}
$