5-12q+3q^2=0

Solution for 5-12q+3q^2=0 equation:

5-12q+3q^2=0

a = 3; b = -12; c = +5;
Δ = b2-4ac
Δ = -122-4·3·5
Δ = 84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{21}}{2*3}=\frac{12-2\sqrt{21}}{6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{21}}{2*3}=\frac{12+2\sqrt{21}}{6}
$