2a(a-7)=16

Solution for 2a(a-7)=16 equation:

2a(a-7)=16

We move all terms to the left:

2a(a-7)-(16)=0

We multiply parentheses

2a^2-14a-16=0

a = 2; b = -14; c = -16;
Δ = b2-4ac
Δ = -142-4·2·(-16)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-18}{2*2}=\frac{-4}{4}
=-1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+18}{2*2}=\frac{32}{4}
=8
$