1/3(12x+21)-5=-1/4(24x-28)

Solution for 1/3(12x+21)-5=-1/4(24x-28) equation:

1/3(12x+21)-5=-1/4(24x-28)

We move all terms to the left:

1/3(12x+21)-5-(-1/4(24x-28))=0


Domain of the equation: 3(12x+21)!=0

x∈R



Domain of the equation: 4(24x-28))!=0

x∈R


We calculate fractions


(4x2/(3(12x+21)*4(24x-28)))+(-(-3x1)/(3(12x+21)*4(24x-28)))-5=0


We calculate terms in parentheses: +(4x2/(3(12x+21)*4(24x-28))), so:

4x2/(3(12x+21)*4(24x-28))

We multiply all the terms by the denominator


4x2

We add all the numbers together, and all the variables

4x^2

Back to the equation:

+(4x^2)



We calculate terms in parentheses: +(-(-3x1)/(3(12x+21)*4(24x-28))), so:

-(-3x1)/(3(12x+21)*4(24x-28))

We add all the numbers together, and all the variables

-(-3x)/(3(12x+21)*4(24x-28))

We multiply all the terms by the denominator


-(-3x)

We get rid of parentheses

3x

Back to the equation:

+(3x)


a = 4; b = 3; c = -5;
Δ = b2-4ac
Δ = 32-4·4·(-5)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{89}}{2*4}=\frac{-3-\sqrt{89}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{89}}{2*4}=\frac{-3+\sqrt{89}}{8}
$