3x^2+27x-123=0

Solution for 3x^2+27x-123=0 equation:

3x^2+27x-123=0

a = 3; b = 27; c = -123;
Δ = b2-4ac
Δ = 272-4·3·(-123)
Δ = 2205
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:

$\sqrt{\Delta}=\sqrt{2205}=\sqrt{441*5}=\sqrt{441}*\sqrt{5}=21\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-21\sqrt{5}}{2*3}=\frac{-27-21\sqrt{5}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+21\sqrt{5}}{2*3}=\frac{-27+21\sqrt{5}}{6}
$