x*(x-1)=1559

Solution for x*(x-1)=1559 equation:

x(x-1)=1559

We move all terms to the left:

x(x-1)-(1559)=0

We multiply parentheses

x^2-1x-1559=0

a = 1; b = -1; c = -1559;
Δ = b2-4ac
Δ = -12-4·1·(-1559)
Δ = 6237
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:

$\sqrt{\Delta}=\sqrt{6237}=\sqrt{81*77}=\sqrt{81}*\sqrt{77}=9\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9\sqrt{77}}{2*1}=\frac{1-9\sqrt{77}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9\sqrt{77}}{2*1}=\frac{1+9\sqrt{77}}{2}
$