x*(x+1)-2651=x+x+1

Solution for x*(x+1)-2651=x+x+1 equation:

x(x+1)-2651=x+x+1

We move all terms to the left:

x(x+1)-2651-(x+x+1)=0

We add all the numbers together, and all the variables

x(x+1)-(2x+1)-2651=0

We multiply parentheses

x^2+x-(2x+1)-2651=0

We get rid of parentheses

x^2+x-2x-1-2651=0

We add all the numbers together, and all the variables

x^2-1x-2652=0

a = 1; b = -1; c = -2652;
Δ = b2-4ac
Δ = -12-4·1·(-2652)
Δ = 10609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10609}=103$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-103}{2*1}=\frac{-102}{2}
=-51
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+103}{2*1}=\frac{104}{2}
=52
$