3p2-10p=1

Solution for 3p2-10p=1 equation:

3p^2-10p=1

We move all terms to the left:

3p^2-10p-(1)=0

a = 3; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·3·(-1)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{7}}{2*3}=\frac{10-4\sqrt{7}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{7}}{2*3}=\frac{10+4\sqrt{7}}{6}
$