2a(a+7)2=36

Solution for 2a(a+7)2=36 equation:

2a(a+7)2=36

We move all terms to the left:

2a(a+7)2-(36)=0

We multiply parentheses

4a^2+28a-36=0

a = 4; b = 28; c = -36;
Δ = b2-4ac
Δ = 282-4·4·(-36)
Δ = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{85}}{2*4}=\frac{-28-4\sqrt{85}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{85}}{2*4}=\frac{-28+4\sqrt{85}}{8}
$