9-p^2=-3+4p

Solution for 9-p^2=-3+4p equation:

9-p^2=-3+4p

We move all terms to the left:

9-p^2-(-3+4p)=0

We add all the numbers together, and all the variables

-p^2-(4p-3)+9=0

We add all the numbers together, and all the variables

-1p^2-(4p-3)+9=0

We get rid of parentheses

-1p^2-4p+3+9=0

We add all the numbers together, and all the variables

-1p^2-4p+12=0

a = -1; b = -4; c = +12;
Δ = b2-4ac
Δ = -42-4·(-1)·12
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-1}=\frac{-4}{-2}
=+2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-1}=\frac{12}{-2}
=-6
$