7(p+3)+9=5(p+2)3p

Solution for 7(p+3)+9=5(p+2)3p equation:

7(p+3)+9=5(p+2)3p

We move all terms to the left:

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

We multiply parentheses

7p-(5(p+2)3p)+21+9=0


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

5(p+2)3p

We multiply parentheses

15p^2+30p

Back to the equation:

-(15p^2+30p)


We add all the numbers together, and all the variables

7p-(15p^2+30p)+30=0

We get rid of parentheses

-15p^2+7p-30p+30=0

We add all the numbers together, and all the variables

-15p^2-23p+30=0

a = -15; b = -23; c = +30;
Δ = b2-4ac
Δ = -232-4·(-15)·30
Δ = 2329
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{-(-23)-\sqrt{2329}}{2*-15}=\frac{23-\sqrt{2329}}{-30}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{2329}}{2*-15}=\frac{23+\sqrt{2329}}{-30}
$