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

We add all the numbers together, and all the variables

18p^2-114p-240=0

a = 18; b = -114; c = -240;
Δ = b2-4ac
Δ = -1142-4·18·(-240)
Δ = 30276
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30276}=174$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-174}{2*18}=\frac{-60}{36}
=-1+2/3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+174}{2*18}=\frac{288}{36}
=8
$