x(x+1)=875

Solution for x(x+1)=875 equation:

x(x+1)=875

We move all terms to the left:

x(x+1)-(875)=0

We multiply parentheses

x^2+x-875=0

a = 1; b = 1; c = -875;
Δ = b2-4ac
Δ = 12-4·1·(-875)
Δ = 3501
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3501}=\sqrt{9*389}=\sqrt{9}*\sqrt{389}=3\sqrt{389}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{389}}{2*1}=\frac{-1-3\sqrt{389}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{389}}{2*1}=\frac{-1+3\sqrt{389}}{2}
$