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

Solution for 21=((x+1)(x))/2 equation:

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

We move all terms to the left:

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

We multiply all the terms by the denominator


-(((x+1)x)+21*2)=0


We calculate terms in parentheses: -(((x+1)x)+21*2), so:

((x+1)x)+21*2

We add all the numbers together, and all the variables

((x+1)x)+42


We calculate terms in parentheses: +((x+1)x), so:

(x+1)x

We multiply parentheses

x^2+x

Back to the equation:

+(x^2+x)


We get rid of parentheses

x^2+x+42

Back to the equation:

-(x^2+x+42)


We get rid of parentheses

-x^2-x-42=0

We add all the numbers together, and all the variables

-1x^2-1x-42=0

a = -1; b = -1; c = -42;
Δ = b2-4ac
Δ = -12-4·(-1)·(-42)
Δ = -167
Delta is less than zero, so there is no solution for the equation