(-9p)(-10+3p)+7p(-9+3p)=0

Solution for (-9p)(-10+3p)+7p(-9+3p)=0 equation:

(-9p)(-10+3p)+7p(-9+3p)=0

We add all the numbers together, and all the variables

(-9p)(3p-10)+7p(3p-9)=0

We multiply parentheses

21p^2+(-9p)(3p-10)-63p=0

We multiply parentheses ..

21p^2+(-27p^2+90p)-63p=0

We get rid of parentheses

21p^2-27p^2+90p-63p=0

We add all the numbers together, and all the variables

-6p^2+27p=0

a = -6; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-6)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-6}=\frac{-54}{-12}
=4+1/2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-6}=\frac{0}{-12}
=0
$