1/3(12x+15)-20=3/4(20x-36)

Solution for 1/3(12x+15)-20=3/4(20x-36) equation:

1/3(12x+15)-20=3/4(20x-36)

We move all terms to the left:

1/3(12x+15)-20-(3/4(20x-36))=0


Domain of the equation: 3(12x+15)!=0

x∈R



Domain of the equation: 4(20x-36))!=0

x∈R


We calculate fractions


(4x2/(3(12x+15)*4(20x-36)))+(-9x1/(3(12x+15)*4(20x-36)))-20=0


We calculate terms in parentheses: +(4x2/(3(12x+15)*4(20x-36))), so:

4x2/(3(12x+15)*4(20x-36))

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: +(-9x1/(3(12x+15)*4(20x-36))), so:

-9x1/(3(12x+15)*4(20x-36))

We multiply all the terms by the denominator


-9x1

We add all the numbers together, and all the variables

-9x

Back to the equation:

+(-9x)


We get rid of parentheses

4x^2-9x-20=0

a = 4; b = -9; c = -20;
Δ = b2-4ac
Δ = -92-4·4·(-20)
Δ = 401
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{-(-9)-\sqrt{401}}{2*4}=\frac{9-\sqrt{401}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{401}}{2*4}=\frac{9+\sqrt{401}}{8}
$