((x-1)x)/2+x=1485

Solution for ((x-1)x)/2+x=1485 equation:

((x-1)x)/2+x=1485

We move all terms to the left:

((x-1)x)/2+x-(1485)=0

We add all the numbers together, and all the variables

x+((x-1)x)/2-1485=0

We multiply all the terms by the denominator


x*2+((x-1)x)-1485*2=0


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

(x-1)x

We multiply parentheses

x^2-1x

Back to the equation:

+(x^2-1x)


We add all the numbers together, and all the variables

x*2+(x^2-1x)-2970=0

Wy multiply elements

2x+(x^2-1x)-2970=0

We get rid of parentheses

x^2+2x-1x-2970=0

We add all the numbers together, and all the variables

x^2+x-2970=0

a = 1; b = 1; c = -2970;
Δ = b2-4ac
Δ = 12-4·1·(-2970)
Δ = 11881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11881}=109$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-109}{2*1}=\frac{-110}{2}
=-55
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+109}{2*1}=\frac{108}{2}
=54
$