-X^2-9x+6=0

Solution for -X^2-9x+6=0 equation:

-X^2-9X+6=0

We add all the numbers together, and all the variables

-1X^2-9X+6=0

a = -1; b = -9; c = +6;
Δ = b2-4ac
Δ = -92-4·(-1)·6
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{105}}{2*-1}=\frac{9-\sqrt{105}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{105}}{2*-1}=\frac{9+\sqrt{105}}{-2}
$