3a(a+4)-2a=7

Solution for 3a(a+4)-2a=7 equation:

3a(a+4)-2a=7

We move all terms to the left:

3a(a+4)-2a-(7)=0

We add all the numbers together, and all the variables

-2a+3a(a+4)-7=0

We multiply parentheses

3a^2-2a+12a-7=0

We add all the numbers together, and all the variables

3a^2+10a-7=0

a = 3; b = 10; c = -7;
Δ = b2-4ac
Δ = 102-4·3·(-7)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{46}}{2*3}=\frac{-10-2\sqrt{46}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{46}}{2*3}=\frac{-10+2\sqrt{46}}{6}
$