x2-x=137

Solution for x2-x=137 equation:

x2-x=137

We move all terms to the left:

x2-x-(137)=0

We add all the numbers together, and all the variables

x^2-1x-137=0

a = 1; b = -1; c = -137;
Δ = b2-4ac
Δ = -12-4·1·(-137)
Δ = 549
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:

$\sqrt{\Delta}=\sqrt{549}=\sqrt{9*61}=\sqrt{9}*\sqrt{61}=3\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{61}}{2*1}=\frac{1-3\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{61}}{2*1}=\frac{1+3\sqrt{61}}{2}
$