3x^2-9x-270=0

Solution for 3x^2-9x-270=0 equation:

3x^2-9x-270=0

a = 3; b = -9; c = -270;
Δ = b2-4ac
Δ = -92-4·3·(-270)
Δ = 3321
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:

$\sqrt{\Delta}=\sqrt{3321}=\sqrt{81*41}=\sqrt{81}*\sqrt{41}=9\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9\sqrt{41}}{2*3}=\frac{9-9\sqrt{41}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9\sqrt{41}}{2*3}=\frac{9+9\sqrt{41}}{6}
$