(x*(x+4))/2=40

Solution for (x*(x+4))/2=40 equation:

(x*(x+4))/2=40

We move all terms to the left:

(x*(x+4))/2-(40)=0

We multiply all the terms by the denominator


(x*(x+4))-40*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)-80=0

We get rid of parentheses

x^2+4x-80=0

a = 1; b = 4; c = -80;
Δ = b2-4ac
Δ = 42-4·1·(-80)
Δ = 336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{21}}{2*1}=\frac{-4-4\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{21}}{2*1}=\frac{-4+4\sqrt{21}}{2}
$