9a^2+3a=6a^2-4a

Solution for 9a^2+3a=6a^2-4a equation:

9a^2+3a=6a^2-4a

We move all terms to the left:

9a^2+3a-(6a^2-4a)=0

We get rid of parentheses

9a^2-6a^2+3a+4a=0

We add all the numbers together, and all the variables

3a^2+7a=0

a = 3; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·3·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*3}=\frac{-14}{6}
=-2+1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*3}=\frac{0}{6}
=0
$