3x^2-21x+15=0

Solution for 3x^2-21x+15=0 equation:

3x^2-21x+15=0

a = 3; b = -21; c = +15;
Δ = b2-4ac
Δ = -212-4·3·15
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{29}}{2*3}=\frac{21-3\sqrt{29}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{29}}{2*3}=\frac{21+3\sqrt{29}}{6}
$