78=(1/2)(n^2-n)

Solution for 78=(1/2)(n^2-n) equation:

78=(1/2)(n^2-n)

We move all terms to the left:

78-((1/2)(n^2-n))=0


Domain of the equation: 2)(n^2-n))!=0

n∈R


We add all the numbers together, and all the variables

-((+1/2)(n^2-n))+78=0

We multiply all the terms by the denominator


-((+1+78*2)(n^2-n))=0


We calculate terms in parentheses: -((+1+78*2)(n^2-n)), so:

(+1+78*2)(n^2-n)

We add all the numbers together, and all the variables

157(n^2-n)

We multiply parentheses

157n^2-157n

Back to the equation:

-(157n^2-157n)


We get rid of parentheses

-157n^2+157n=0

a = -157; b = 157; c = 0;
Δ = b2-4ac
Δ = 1572-4·(-157)·0
Δ = 24649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24649}=157$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(157)-157}{2*-157}=\frac{-314}{-314}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(157)+157}{2*-157}=\frac{0}{-314}
=0
$