(x(x+7))/2=30

Solution for (x(x+7))/2=30 equation:

(x(x+7))/2=30

We move all terms to the left:

(x(x+7))/2-(30)=0

We multiply all the terms by the denominator


(x(x+7))-30*2=0


We calculate terms in parentheses: +(x(x+7)), so:

x(x+7)

We multiply parentheses

x^2+7x

Back to the equation:

+(x^2+7x)


We add all the numbers together, and all the variables

(x^2+7x)-60=0

We get rid of parentheses

x^2+7x-60=0

a = 1; b = 7; c = -60;
Δ = b2-4ac
Δ = 72-4·1·(-60)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-17}{2*1}=\frac{-24}{2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+17}{2*1}=\frac{10}{2}
=5
$