3x2-12x-21x=84

Solution for 3x2-12x-21x=84 equation:

3x^2-12x-21x=84

We move all terms to the left:

3x^2-12x-21x-(84)=0

We add all the numbers together, and all the variables

3x^2-33x-84=0

a = 3; b = -33; c = -84;
Δ = b2-4ac
Δ = -332-4·3·(-84)
Δ = 2097
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:

$\sqrt{\Delta}=\sqrt{2097}=\sqrt{9*233}=\sqrt{9}*\sqrt{233}=3\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{233}}{2*3}=\frac{33-3\sqrt{233}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{233}}{2*3}=\frac{33+3\sqrt{233}}{6}
$