12(5+4p)7p=6(8p-4)

Solution for 12(5+4p)7p=6(8p-4) equation:

12(5+4p)7p=6(8p-4)

We move all terms to the left:

12(5+4p)7p-(6(8p-4))=0

We add all the numbers together, and all the variables

12(4p+5)7p-(6(8p-4))=0

We multiply parentheses

336p^2+420p-(6(8p-4))=0


We calculate terms in parentheses: -(6(8p-4)), so:

6(8p-4)

We multiply parentheses

48p-24

Back to the equation:

-(48p-24)


We get rid of parentheses

336p^2+420p-48p+24=0

We add all the numbers together, and all the variables

336p^2+372p+24=0

a = 336; b = 372; c = +24;
Δ = b2-4ac
Δ = 3722-4·336·24
Δ = 106128
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:

$\sqrt{\Delta}=\sqrt{106128}=\sqrt{144*737}=\sqrt{144}*\sqrt{737}=12\sqrt{737}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(372)-12\sqrt{737}}{2*336}=\frac{-372-12\sqrt{737}}{672}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(372)+12\sqrt{737}}{2*336}=\frac{-372+12\sqrt{737}}{672}
$