-3x^2-30x-67=0

Solution for -3x^2-30x-67=0 equation:

-3x^2-30x-67=0

a = -3; b = -30; c = -67;
Δ = b2-4ac
Δ = -302-4·(-3)·(-67)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-4\sqrt{6}}{2*-3}=\frac{30-4\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+4\sqrt{6}}{2*-3}=\frac{30+4\sqrt{6}}{-6}
$