24x^2+18x+2=0

Solution for 24x^2+18x+2=0 equation:

24x^2+18x+2=0

a = 24; b = 18; c = +2;
Δ = b2-4ac
Δ = 182-4·24·2
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{33}}{2*24}=\frac{-18-2\sqrt{33}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{33}}{2*24}=\frac{-18+2\sqrt{33}}{48}
$