x(x+1)=702

Solution for x(x+1)=702 equation:

x(x+1)=702

We move all terms to the left:

x(x+1)-(702)=0

We multiply parentheses

x^2+x-702=0

a = 1; b = 1; c = -702;
Δ = b2-4ac
Δ = 12-4·1·(-702)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-53}{2*1}=\frac{-54}{2}
=-27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+53}{2*1}=\frac{52}{2}
=26
$