x(x+1)=2970

Solution for x(x+1)=2970 equation:

x(x+1)=2970

We move all terms to the left:

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

We multiply parentheses

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
$