20-2p=2/3p-4

Solution for 20-2p=2/3p-4 equation:

20-2p=2/3p-4

We move all terms to the left:

20-2p-(2/3p-4)=0


Domain of the equation: 3p-4)!=0

p∈R


We get rid of parentheses

-2p-2/3p+4+20=0

We multiply all the terms by the denominator


-2p*3p+4*3p+20*3p-2=0

Wy multiply elements

-6p^2+12p+60p-2=0

We add all the numbers together, and all the variables

-6p^2+72p-2=0

a = -6; b = 72; c = -2;
Δ = b2-4ac
Δ = 722-4·(-6)·(-2)
Δ = 5136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5136}=\sqrt{16*321}=\sqrt{16}*\sqrt{321}=4\sqrt{321}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-4\sqrt{321}}{2*-6}=\frac{-72-4\sqrt{321}}{-12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+4\sqrt{321}}{2*-6}=\frac{-72+4\sqrt{321}}{-12}
$