x(x+1)=2070

Solution for x(x+1)=2070 equation:

x(x+1)=2070

We move all terms to the left:

x(x+1)-(2070)=0

We multiply parentheses

x^2+x-2070=0

a = 1; b = 1; c = -2070;
Δ = b2-4ac
Δ = 12-4·1·(-2070)
Δ = 8281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8281}=91$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-91}{2*1}=\frac{-92}{2}
=-46
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+91}{2*1}=\frac{90}{2}
=45
$