12-2a=3a(a-6)

Solution for 12-2a=3a(a-6) equation:

12-2a=3a(a-6)

We move all terms to the left:

12-2a-(3a(a-6))=0


We calculate terms in parentheses: -(3a(a-6)), so:

3a(a-6)

We multiply parentheses

3a^2-18a

Back to the equation:

-(3a^2-18a)


We get rid of parentheses

-3a^2-2a+18a+12=0

We add all the numbers together, and all the variables

-3a^2+16a+12=0

a = -3; b = 16; c = +12;
Δ = b2-4ac
Δ = 162-4·(-3)·12
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-20}{2*-3}=\frac{-36}{-6}
=+6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+20}{2*-3}=\frac{4}{-6}
=-2/3
$