3p^2+10p+6=0

Solution for 3p^2+10p+6=0 equation:

3p^2+10p+6=0

a = 3; b = 10; c = +6;
Δ = b2-4ac
Δ = 102-4·3·6
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{7}}{2*3}=\frac{-10-2\sqrt{7}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{7}}{2*3}=\frac{-10+2\sqrt{7}}{6}
$