(X(x+4))/2=30

Solution for (X(x+4))/2=30 equation:

(X(X+4))/2=30

We move all terms to the left:

(X(X+4))/2-(30)=0

We multiply all the terms by the denominator


(X(X+4))-30*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)-60=0

We get rid of parentheses

X^2+4X-60=0

a = 1; b = 4; c = -60;
Δ = b2-4ac
Δ = 42-4·1·(-60)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-16}{2*1}=\frac{-20}{2}
=-10
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+16}{2*1}=\frac{12}{2}
=6
$