6x^2-9x-64=0

Solution for 6x^2-9x-64=0 equation:

6x^2-9x-64=0

a = 6; b = -9; c = -64;
Δ = b2-4ac
Δ = -92-4·6·(-64)
Δ = 1617
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:

$\sqrt{\Delta}=\sqrt{1617}=\sqrt{49*33}=\sqrt{49}*\sqrt{33}=7\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-7\sqrt{33}}{2*6}=\frac{9-7\sqrt{33}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7\sqrt{33}}{2*6}=\frac{9+7\sqrt{33}}{12}
$