3r^2-15r+3=0

Solution for 3r^2-15r+3=0 equation:

3r^2-15r+3=0

a = 3; b = -15; c = +3;
Δ = b2-4ac
Δ = -152-4·3·3
Δ = 189
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{21}}{2*3}=\frac{15-3\sqrt{21}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{21}}{2*3}=\frac{15+3\sqrt{21}}{6}
$