(a(a+2))=48

Solution for (a(a+2))=48 equation:

(a(a+2))=48

We move all terms to the left:

(a(a+2))-(48)=0


We calculate terms in parentheses: +(a(a+2)), so:

a(a+2)

We multiply parentheses

a^2+2a

Back to the equation:

+(a^2+2a)


We get rid of parentheses

a^2+2a-48=0

a = 1; b = 2; c = -48;
Δ = b2-4ac
Δ = 22-4·1·(-48)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*1}=\frac{-16}{2}
=-8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*1}=\frac{12}{2}
=6
$