(-6p+8)(7p+9)=0

Solution for (-6p+8)(7p+9)=0 equation:

(-6p+8)(7p+9)=0

We multiply parentheses ..

(-42p^2-54p+56p+72)=0

We get rid of parentheses

-42p^2-54p+56p+72=0

We add all the numbers together, and all the variables

-42p^2+2p+72=0

a = -42; b = 2; c = +72;
Δ = b2-4ac
Δ = 22-4·(-42)·72
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-110}{2*-42}=\frac{-112}{-84}
=1+1/3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+110}{2*-42}=\frac{108}{-84}
=-1+2/7
$