6p(p-2)+4(8-p)=22

Solution for 6p(p-2)+4(8-p)=22 equation:

6p(p-2)+4(8-p)=22

We move all terms to the left:

6p(p-2)+4(8-p)-(22)=0

We add all the numbers together, and all the variables

6p(p-2)+4(-1p+8)-22=0

We multiply parentheses

6p^2-12p-4p+32-22=0

We add all the numbers together, and all the variables

6p^2-16p+10=0

a = 6; b = -16; c = +10;
Δ = b2-4ac
Δ = -162-4·6·10
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4}{2*6}=\frac{12}{12}
=1
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4}{2*6}=\frac{20}{12}
=1+2/3
$