2p(4p-5)/3=4

Solution for 2p(4p-5)/3=4 equation:

2p(4p-5)/3=4

We move all terms to the left:

2p(4p-5)/3-(4)=0

We multiply all the terms by the denominator


2p(4p-5)-4*3=0

We add all the numbers together, and all the variables

2p(4p-5)-12=0

We multiply parentheses

8p^2-10p-12=0

a = 8; b = -10; c = -12;
Δ = b2-4ac
Δ = -102-4·8·(-12)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-22}{2*8}=\frac{-12}{16}
=-3/4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+22}{2*8}=\frac{32}{16}
=2
$