x^2-x-47=0

Solution for x^2-x-47=0 equation:

x^2-x-47=0

We add all the numbers together, and all the variables

x^2-1x-47=0

a = 1; b = -1; c = -47;
Δ = b2-4ac
Δ = -12-4·1·(-47)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{21}}{2*1}=\frac{1-3\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{21}}{2*1}=\frac{1+3\sqrt{21}}{2}
$