20a-16=12(3-a)a=

Solution for 20a-16=12(3-a)a= equation:

20a-16=12(3-a)a=

We move all terms to the left:

20a-16-(12(3-a)a)=0

We add all the numbers together, and all the variables

20a-(12(-1a+3)a)-16=0


We calculate terms in parentheses: -(12(-1a+3)a), so:

12(-1a+3)a

We multiply parentheses

-12a^2+36a

Back to the equation:

-(-12a^2+36a)


We get rid of parentheses

12a^2-36a+20a-16=0

We add all the numbers together, and all the variables

12a^2-16a-16=0

a = 12; b = -16; c = -16;
Δ = b2-4ac
Δ = -162-4·12·(-16)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-32}{2*12}=\frac{-16}{24}
=-2/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+32}{2*12}=\frac{48}{24}
=2
$