2r^2-12r-64=0

Solution for 2r^2-12r-64=0 equation:

2r^2-12r-64=0

a = 2; b = -12; c = -64;
Δ = b2-4ac
Δ = -122-4·2·(-64)
Δ = 656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{41}}{2*2}=\frac{12-4\sqrt{41}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{41}}{2*2}=\frac{12+4\sqrt{41}}{4}
$