(p-6)(8p-5)=0

Solution for (p-6)(8p-5)=0 equation:

(p-6)(8p-5)=0

We multiply parentheses ..

(+8p^2-5p-48p+30)=0

We get rid of parentheses

8p^2-5p-48p+30=0

We add all the numbers together, and all the variables

8p^2-53p+30=0

a = 8; b = -53; c = +30;
Δ = b2-4ac
Δ = -532-4·8·30
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-43}{2*8}=\frac{10}{16}
=5/8
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+43}{2*8}=\frac{96}{16}
=6
$