9x2+24x+14=0

Solution for 9x2+24x+14=0 equation:

9x^2+24x+14=0

a = 9; b = 24; c = +14;
Δ = b2-4ac
Δ = 242-4·9·14
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{2}}{2*9}=\frac{-24-6\sqrt{2}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{2}}{2*9}=\frac{-24+6\sqrt{2}}{18}
$