4a+3a(a+1)=24

Solution for 4a+3a(a+1)=24 equation:

4a+3a(a+1)=24

We move all terms to the left:

4a+3a(a+1)-(24)=0

We multiply parentheses

3a^2+4a+3a-24=0

We add all the numbers together, and all the variables

3a^2+7a-24=0

a = 3; b = 7; c = -24;
Δ = b2-4ac
Δ = 72-4·3·(-24)
Δ = 337
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{-(7)-\sqrt{337}}{2*3}=\frac{-7-\sqrt{337}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{337}}{2*3}=\frac{-7+\sqrt{337}}{6}
$