3x^2-84x-9261=0

Solution for 3x^2-84x-9261=0 equation:

3x^2-84x-9261=0

a = 3; b = -84; c = -9261;
Δ = b2-4ac
Δ = -842-4·3·(-9261)
Δ = 118188
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:

$\sqrt{\Delta}=\sqrt{118188}=\sqrt{1764*67}=\sqrt{1764}*\sqrt{67}=42\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-42\sqrt{67}}{2*3}=\frac{84-42\sqrt{67}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+42\sqrt{67}}{2*3}=\frac{84+42\sqrt{67}}{6}
$