x^2-x=4.75

Solution for x^2-x=4.75 equation:

x^2-x=4.75

We move all terms to the left:

x^2-x-(4.75)=0

We add all the numbers together, and all the variables

x^2-1x-4.75=0

a = 1; b = -1; c = -4.75;
Δ = b2-4ac
Δ = -12-4·1·(-4.75)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-2\sqrt{5}}{2*1}=\frac{1-2\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+2\sqrt{5}}{2*1}=\frac{1+2\sqrt{5}}{2}
$