1/3(27x+15)-1=-3/4(28x-12)

Solution for 1/3(27x+15)-1=-3/4(28x-12) equation:

1/3(27x+15)-1=-3/4(28x-12)

We move all terms to the left:

1/3(27x+15)-1-(-3/4(28x-12))=0


Domain of the equation: 3(27x+15)!=0

x∈R



Domain of the equation: 4(28x-12))!=0

x∈R


We calculate fractions


(4x2/(3(27x+15)*4(28x-12)))+(-(-9x2)/(3(27x+15)*4(28x-12)))-1=0


We calculate terms in parentheses: +(4x2/(3(27x+15)*4(28x-12))), so:

4x2/(3(27x+15)*4(28x-12))

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: +(-(-9x2)/(3(27x+15)*4(28x-12))), so:

-(-9x2)/(3(27x+15)*4(28x-12))

We add all the numbers together, and all the variables

-(-9x^2)/(3(27x+15)*4(28x-12))

We multiply all the terms by the denominator


-(-9x^2)

We get rid of parentheses

9x^2

Back to the equation:

+(9x^2)


We add all the numbers together, and all the variables

13x^2-1=0

a = 13; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·13·(-1)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{13}}{2*13}=\frac{0-2\sqrt{13}}{26}
=-\frac{2\sqrt{13}}{26}
=-\frac{\sqrt{13}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{13}}{2*13}=\frac{0+2\sqrt{13}}{26}
=\frac{2\sqrt{13}}{26}
=\frac{\sqrt{13}}{13}
$