72x^2+24x+1=0

Solution for 72x^2+24x+1=0 equation:

72x^2+24x+1=0

a = 72; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·72·1
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12\sqrt{2}}{2*72}=\frac{-24-12\sqrt{2}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{2}}{2*72}=\frac{-24+12\sqrt{2}}{144}
$