15p^2-107p=3p^2+240+7p

Solution for 15p^2-107p=3p^2+240+7p equation:

15p^2-107p=3p^2+240+7p

We move all terms to the left:

15p^2-107p-(3p^2+240+7p)=0

We get rid of parentheses

15p^2-3p^2-107p-7p-240=0

We add all the numbers together, and all the variables

12p^2-114p-240=0

a = 12; b = -114; c = -240;
Δ = b2-4ac
Δ = -1142-4·12·(-240)
Δ = 24516
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:

$\sqrt{\Delta}=\sqrt{24516}=\sqrt{36*681}=\sqrt{36}*\sqrt{681}=6\sqrt{681}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-6\sqrt{681}}{2*12}=\frac{114-6\sqrt{681}}{24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+6\sqrt{681}}{2*12}=\frac{114+6\sqrt{681}}{24}
$