24x^2+78x+9=0

Solution for 24x^2+78x+9=0 equation:

24x^2+78x+9=0

a = 24; b = 78; c = +9;
Δ = b2-4ac
Δ = 782-4·24·9
Δ = 5220
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:

$\sqrt{\Delta}=\sqrt{5220}=\sqrt{36*145}=\sqrt{36}*\sqrt{145}=6\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-6\sqrt{145}}{2*24}=\frac{-78-6\sqrt{145}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+6\sqrt{145}}{2*24}=\frac{-78+6\sqrt{145}}{48}
$