2p-9=3(p2-5)

Solution for 2p-9=3(p2-5) equation:

2p-9=3(p2-5)

We move all terms to the left:

2p-9-(3(p2-5))=0

We add all the numbers together, and all the variables

-(3(+p^2-5))+2p-9=0


We calculate terms in parentheses: -(3(+p^2-5)), so:

3(+p^2-5)

We multiply parentheses

3p^2-15

Back to the equation:

-(3p^2-15)


We add all the numbers together, and all the variables

2p-(3p^2-15)-9=0

We get rid of parentheses

-3p^2+2p+15-9=0

We add all the numbers together, and all the variables

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

a = -3; b = 2; c = +6;
Δ = b2-4ac
Δ = 22-4·(-3)·6
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{19}}{2*-3}=\frac{-2-2\sqrt{19}}{-6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{19}}{2*-3}=\frac{-2+2\sqrt{19}}{-6}
$