2a(a-4)=3a+6

Solution for 2a(a-4)=3a+6 equation:

2a(a-4)=3a+6

We move all terms to the left:

2a(a-4)-(3a+6)=0

We multiply parentheses

2a^2-8a-(3a+6)=0

We get rid of parentheses

2a^2-8a-3a-6=0

We add all the numbers together, and all the variables

2a^2-11a-6=0

a = 2; b = -11; c = -6;
Δ = b2-4ac
Δ = -112-4·2·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-13}{2*2}=\frac{-2}{4}
=-1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+13}{2*2}=\frac{24}{4}
=6
$