3a^2+9a=7

Solution for 3a^2+9a=7 equation:

3a^2+9a=7

We move all terms to the left:

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

a = 3; b = 9; c = -7;
Δ = b2-4ac
Δ = 92-4·3·(-7)
Δ = 165
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{165}}{2*3}=\frac{-9-\sqrt{165}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{165}}{2*3}=\frac{-9+\sqrt{165}}{6}
$