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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6a^2+5a-4=0

a = 6; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·6·(-4)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*6}=\frac{-16}{12}
=-1+1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*6}=\frac{6}{12}
=1/2
$