3(5p-6)+4(20-3p)p=4

Solution for 3(5p-6)+4(20-3p)p=4 equation:

3(5p-6)+4(20-3p)p=4

We move all terms to the left:

3(5p-6)+4(20-3p)p-(4)=0

We add all the numbers together, and all the variables

3(5p-6)+4(-3p+20)p-4=0

We multiply parentheses

-12p^2+15p+80p-18-4=0

We add all the numbers together, and all the variables

-12p^2+95p-22=0

a = -12; b = 95; c = -22;
Δ = b2-4ac
Δ = 952-4·(-12)·(-22)
Δ = 7969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(95)-\sqrt{7969}}{2*-12}=\frac{-95-\sqrt{7969}}{-24}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(95)+\sqrt{7969}}{2*-12}=\frac{-95+\sqrt{7969}}{-24}
$