(x(x+4))/2=16

Solution for (x(x+4))/2=16 equation:

(x(x+4))/2=16

We move all terms to the left:

(x(x+4))/2-(16)=0

We multiply all the terms by the denominator


(x(x+4))-16*2=0


We calculate terms in parentheses: +(x(x+4)), so:

x(x+4)

We multiply parentheses

x^2+4x

Back to the equation:

+(x^2+4x)


We add all the numbers together, and all the variables

(x^2+4x)-32=0

We get rid of parentheses

x^2+4x-32=0

a = 1; b = 4; c = -32;
Δ = b2-4ac
Δ = 42-4·1·(-32)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12}{2*1}=\frac{8}{2}
=4
$