x(x-1)=342

Solution for x(x-1)=342 equation:

x(x-1)=342

We move all terms to the left:

x(x-1)-(342)=0

We multiply parentheses

x^2-1x-342=0

a = 1; b = -1; c = -342;
Δ = b2-4ac
Δ = -12-4·1·(-342)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-37}{2*1}=\frac{-36}{2}
=-18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+37}{2*1}=\frac{38}{2}
=19
$