9a^2-40a+24=0

Solution for 9a^2-40a+24=0 equation:

9a^2-40a+24=0

a = 9; b = -40; c = +24;
Δ = b2-4ac
Δ = -402-4·9·24
Δ = 736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{46}}{2*9}=\frac{40-4\sqrt{46}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{46}}{2*9}=\frac{40+4\sqrt{46}}{18}
$