-X^2-34x-27=0

Solution for -X^2-34x-27=0 equation:

-X^2-34X-27=0

We add all the numbers together, and all the variables

-1X^2-34X-27=0

a = -1; b = -34; c = -27;
Δ = b2-4ac
Δ = -342-4·(-1)·(-27)
Δ = 1048
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:

$\sqrt{\Delta}=\sqrt{1048}=\sqrt{4*262}=\sqrt{4}*\sqrt{262}=2\sqrt{262}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{262}}{2*-1}=\frac{34-2\sqrt{262}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{262}}{2*-1}=\frac{34+2\sqrt{262}}{-2}
$