(x(x+1)/2)=17.875

Solution for (x(x+1)/2)=17.875 equation:

(x(x+1)/2)=17.875

We move all terms to the left:

(x(x+1)/2)-(17.875)=0

We add all the numbers together, and all the variables

(x(x+1)/2)-17.875=0

We multiply all the terms by the denominator


(x(x+1)-(17.875)*2)=0


We calculate terms in parentheses: +(x(x+1)-(17.875)*2), so:

x(x+1)-(17.875)*2

We add all the numbers together, and all the variables

x(x+1)-35.75

We multiply parentheses

x^2+x-35.75

Back to the equation:

+(x^2+x-35.75)


We get rid of parentheses

x^2+x-35.75=0

a = 1; b = 1; c = -35.75;
Δ = b2-4ac
Δ = 12-4·1·(-35.75)
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{-(1)-12}{2*1}=\frac{-13}{2}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+12}{2*1}=\frac{11}{2}
=5+1/2
$