x(x+1)=1560

Solution for x(x+1)=1560 equation:

x(x+1)=1560

We move all terms to the left:

x(x+1)-(1560)=0

We multiply parentheses

x^2+x-1560=0

a = 1; b = 1; c = -1560;
Δ = b2-4ac
Δ = 12-4·1·(-1560)
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-79}{2*1}=\frac{-80}{2}
=-40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+79}{2*1}=\frac{78}{2}
=39
$