12c^2-24c+5=0

Solution for 12c^2-24c+5=0 equation:

12c^2-24c+5=0

a = 12; b = -24; c = +5;
Δ = b2-4ac
Δ = -242-4·12·5
Δ = 336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{21}}{2*12}=\frac{24-4\sqrt{21}}{24}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{21}}{2*12}=\frac{24+4\sqrt{21}}{24}
$