(x)(x+1)=323

Solution for (x)(x+1)=323 equation:

(x)(x+1)=323

We move all terms to the left:

(x)(x+1)-(323)=0

We multiply parentheses

x^2+x-323=0

a = 1; b = 1; c = -323;
Δ = b2-4ac
Δ = 12-4·1·(-323)
Δ = 1293
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{1293}}{2*1}=\frac{-1-\sqrt{1293}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1293}}{2*1}=\frac{-1+\sqrt{1293}}{2}
$