1/4(12x+36)-15=-1/5(20x-35)

Solution for 1/4(12x+36)-15=-1/5(20x-35) equation:

1/4(12x+36)-15=-1/5(20x-35)

We move all terms to the left:

1/4(12x+36)-15-(-1/5(20x-35))=0


Domain of the equation: 4(12x+36)!=0

x∈R



Domain of the equation: 5(20x-35))!=0

x∈R


We calculate fractions


(5x2/(4(12x+36)*5(20x-35)))+(-(-4x1)/(4(12x+36)*5(20x-35)))-15=0


We calculate terms in parentheses: +(5x2/(4(12x+36)*5(20x-35))), so:

5x2/(4(12x+36)*5(20x-35))

We multiply all the terms by the denominator


5x2

We add all the numbers together, and all the variables

5x^2

Back to the equation:

+(5x^2)



We calculate terms in parentheses: +(-(-4x1)/(4(12x+36)*5(20x-35))), so:

-(-4x1)/(4(12x+36)*5(20x-35))

We add all the numbers together, and all the variables

-(-4x)/(4(12x+36)*5(20x-35))

We multiply all the terms by the denominator


-(-4x)

We get rid of parentheses

4x

Back to the equation:

+(4x)


a = 5; b = 4; c = -15;
Δ = b2-4ac
Δ = 42-4·5·(-15)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{79}}{2*5}=\frac{-4-2\sqrt{79}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{79}}{2*5}=\frac{-4+2\sqrt{79}}{10}
$