2a+7a(a+3)=84

Solution for 2a+7a(a+3)=84 equation:

2a+7a(a+3)=84

We move all terms to the left:

2a+7a(a+3)-(84)=0

We multiply parentheses

7a^2+2a+21a-84=0

We add all the numbers together, and all the variables

7a^2+23a-84=0

a = 7; b = 23; c = -84;
Δ = b2-4ac
Δ = 232-4·7·(-84)
Δ = 2881
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{-(23)-\sqrt{2881}}{2*7}=\frac{-23-\sqrt{2881}}{14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{2881}}{2*7}=\frac{-23+\sqrt{2881}}{14}
$