15p^2+2p=5p^2+9

Solution for 15p^2+2p=5p^2+9 equation:

15p^2+2p=5p^2+9

We move all terms to the left:

15p^2+2p-(5p^2+9)=0

We get rid of parentheses

15p^2-5p^2+2p-9=0

We add all the numbers together, and all the variables

10p^2+2p-9=0

a = 10; b = 2; c = -9;
Δ = b2-4ac
Δ = 22-4·10·(-9)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{91}}{2*10}=\frac{-2-2\sqrt{91}}{20}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{91}}{2*10}=\frac{-2+2\sqrt{91}}{20}
$