66-x^2-x=10

Solution for 66-x^2-x=10 equation:

66-x^2-x=10

We move all terms to the left:

66-x^2-x-(10)=0

We add all the numbers together, and all the variables

-1x^2-1x+56=0

a = -1; b = -1; c = +56;
Δ = b2-4ac
Δ = -12-4·(-1)·56
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-15}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+15}{2*-1}=\frac{16}{-2}
=-8
$