1/4(28a-12)=3/5(5+10a)

Solution for 1/4(28a-12)=3/5(5+10a) equation:

1/4(28a-12)=3/5(5+10a)

We move all terms to the left:

1/4(28a-12)-(3/5(5+10a))=0


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

a∈R



Domain of the equation: 5(5+10a))!=0

a∈R


We add all the numbers together, and all the variables

1/4(28a-12)-(3/5(10a+5))=0

We calculate fractions


(5a1/(4(28a-12)*5(10a+5)))+(-12a2/(4(28a-12)*5(10a+5)))=0


We calculate terms in parentheses: +(5a1/(4(28a-12)*5(10a+5))), so:

5a1/(4(28a-12)*5(10a+5))

We multiply all the terms by the denominator


5a1

We add all the numbers together, and all the variables

5a

Back to the equation:

+(5a)



We calculate terms in parentheses: +(-12a2/(4(28a-12)*5(10a+5))), so:

-12a2/(4(28a-12)*5(10a+5))

We multiply all the terms by the denominator


-12a2

We add all the numbers together, and all the variables

-12a^2

Back to the equation:

+(-12a^2)


We get rid of parentheses

-12a^2+5a=0

a = -12; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-12)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-12}=\frac{-10}{-24}
=5/12
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-12}=\frac{0}{-24}
=0
$