3a(a+4)-2a+7=9

Solution for 3a(a+4)-2a+7=9 equation:

3a(a+4)-2a+7=9

We move all terms to the left:

3a(a+4)-2a+7-(9)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

3a^2+10a-2=0

a = 3; b = 10; c = -2;
Δ = b2-4ac
Δ = 102-4·3·(-2)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{31}}{2*3}=\frac{-10-2\sqrt{31}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{31}}{2*3}=\frac{-10+2\sqrt{31}}{6}
$