2a^2+6a+9=87

Solution for 2a^2+6a+9=87 equation:

2a^2+6a+9=87

We move all terms to the left:

2a^2+6a+9-(87)=0

We add all the numbers together, and all the variables

2a^2+6a-78=0

a = 2; b = 6; c = -78;
Δ = b2-4ac
Δ = 62-4·2·(-78)
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{165}}{2*2}=\frac{-6-2\sqrt{165}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{165}}{2*2}=\frac{-6+2\sqrt{165}}{4}
$