8x^2-72x-9=0

Solution for 8x^2-72x-9=0 equation:

8x^2-72x-9=0

a = 8; b = -72; c = -9;
Δ = b2-4ac
Δ = -722-4·8·(-9)
Δ = 5472
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:

$\sqrt{\Delta}=\sqrt{5472}=\sqrt{144*38}=\sqrt{144}*\sqrt{38}=12\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{38}}{2*8}=\frac{72-12\sqrt{38}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{38}}{2*8}=\frac{72+12\sqrt{38}}{16}
$