3a(a-2)=3a+36

Solution for 3a(a-2)=3a+36 equation:

3a(a-2)=3a+36

We move all terms to the left:

3a(a-2)-(3a+36)=0

We multiply parentheses

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

We get rid of parentheses

3a^2-6a-3a-36=0

We add all the numbers together, and all the variables

3a^2-9a-36=0

a = 3; b = -9; c = -36;
Δ = b2-4ac
Δ = -92-4·3·(-36)
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{57}}{2*3}=\frac{9-3\sqrt{57}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{57}}{2*3}=\frac{9+3\sqrt{57}}{6}
$