9p+7=6p2+3p

Solution for 9p+7=6p2+3p equation:

9p+7=6p^2+3p

We move all terms to the left:

9p+7-(6p^2+3p)=0

We get rid of parentheses

-6p^2+9p-3p+7=0

We add all the numbers together, and all the variables

-6p^2+6p+7=0

a = -6; b = 6; c = +7;
Δ = b2-4ac
Δ = 62-4·(-6)·7
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{51}}{2*-6}=\frac{-6-2\sqrt{51}}{-12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{51}}{2*-6}=\frac{-6+2\sqrt{51}}{-12}
$