31p+10p+1=6p^2

Solution for 31p+10p+1=6p^2 equation:

31p+10p+1=6p^2

We move all terms to the left:

31p+10p+1-(6p^2)=0

determiningTheFunctionDomain
-6p^2+31p+10p+1=0

We add all the numbers together, and all the variables

-6p^2+41p+1=0

a = -6; b = 41; c = +1;
Δ = b2-4ac
Δ = 412-4·(-6)·1
Δ = 1705
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-\sqrt{1705}}{2*-6}=\frac{-41-\sqrt{1705}}{-12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+\sqrt{1705}}{2*-6}=\frac{-41+\sqrt{1705}}{-12}
$