8x^2-72x+40=0

Solution for 8x^2-72x+40=0 equation:

8x^2-72x+40=0

a = 8; b = -72; c = +40;
Δ = b2-4ac
Δ = -722-4·8·40
Δ = 3904
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:

$\sqrt{\Delta}=\sqrt{3904}=\sqrt{64*61}=\sqrt{64}*\sqrt{61}=8\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{61}}{2*8}=\frac{72-8\sqrt{61}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{61}}{2*8}=\frac{72+8\sqrt{61}}{16}
$