6p^2=7+19p

Solution for 6p^2=7+19p equation:

6p^2=7+19p

We move all terms to the left:

6p^2-(7+19p)=0

We add all the numbers together, and all the variables

6p^2-(19p+7)=0

We get rid of parentheses

6p^2-19p-7=0

a = 6; b = -19; c = -7;
Δ = b2-4ac
Δ = -192-4·6·(-7)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-23}{2*6}=\frac{-4}{12}
=-1/3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+23}{2*6}=\frac{42}{12}
=3+1/2
$