6(6-2a)=-27a-(3/2)(-4a+6)

Solution for 6(6-2a)=-27a-(3/2)(-4a+6) equation:

6(6-2a)=-27a-(3/2)(-4a+6)

We move all terms to the left:

6(6-2a)-(-27a-(3/2)(-4a+6))=0


Domain of the equation: 2)(-4a+6))!=0

a∈R


We add all the numbers together, and all the variables

6(-2a+6)-(-27a-(+3/2)(-4a+6))=0

We multiply parentheses

-12a-(-27a-(+3/2)(-4a+6))+36=0

We multiply parentheses ..

-(-27a-(-12a^2+3/2*6))-12a+36=0

We multiply all the terms by the denominator


-(-27a-(-12a^2+3-12a*2*6))+36*2*6))=0


We calculate terms in parentheses: -(-27a-(-12a^2+3-12a*2*6)), so:

-27a-(-12a^2+3-12a*2*6)

determiningTheFunctionDomain
-(-12a^2+3-12a*2*6)-27a

We get rid of parentheses

12a^2+12a*2*6-27a-3

We add all the numbers together, and all the variables

12a^2-27a+12a*2*6-3

Wy multiply elements

12a^2-27a+144a*6-3

Wy multiply elements

12a^2-27a+864a-3

We add all the numbers together, and all the variables

12a^2+837a-3

Back to the equation:

-(12a^2+837a-3)


We add all the numbers together, and all the variables

-(12a^2+837a-3)=0

We get rid of parentheses

-12a^2-837a+3=0

a = -12; b = -837; c = +3;
Δ = b2-4ac
Δ = -8372-4·(-12)·3
Δ = 700713
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{700713}=\sqrt{9*77857}=\sqrt{9}*\sqrt{77857}=3\sqrt{77857}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-837)-3\sqrt{77857}}{2*-12}=\frac{837-3\sqrt{77857}}{-24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-837)+3\sqrt{77857}}{2*-12}=\frac{837+3\sqrt{77857}}{-24}
$