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

Solution for (3p-7)(5p+9)=0 equation:

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

We multiply parentheses ..

(+15p^2+27p-35p-63)=0

We get rid of parentheses

15p^2+27p-35p-63=0

We add all the numbers together, and all the variables

15p^2-8p-63=0

a = 15; b = -8; c = -63;
Δ = b2-4ac
Δ = -82-4·15·(-63)
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-62}{2*15}=\frac{-54}{30}
=-1+4/5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+62}{2*15}=\frac{70}{30}
=2+1/3
$