-6x^2-36x-42=0

Solution for -6x^2-36x-42=0 equation:

-6x^2-36x-42=0

a = -6; b = -36; c = -42;
Δ = b2-4ac
Δ = -362-4·(-6)·(-42)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{2}}{2*-6}=\frac{36-12\sqrt{2}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{2}}{2*-6}=\frac{36+12\sqrt{2}}{-12}
$