-10x^2-10x-1=0

Solution for -10x^2-10x-1=0 equation:

-10x^2-10x-1=0

a = -10; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·(-10)·(-1)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{15}}{2*-10}=\frac{10-2\sqrt{15}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{15}}{2*-10}=\frac{10+2\sqrt{15}}{-20}
$