-9x^2-45x+486=0

Solution for -9x^2-45x+486=0 equation:

-9x^2-45x+486=0

a = -9; b = -45; c = +486;
Δ = b2-4ac
Δ = -452-4·(-9)·486
Δ = 19521
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:

$\sqrt{\Delta}=\sqrt{19521}=\sqrt{81*241}=\sqrt{81}*\sqrt{241}=9\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-9\sqrt{241}}{2*-9}=\frac{45-9\sqrt{241}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+9\sqrt{241}}{2*-9}=\frac{45+9\sqrt{241}}{-18}
$