92=4p(6p-3)

Solution for 92=4p(6p-3) equation:

92=4p(6p-3)

We move all terms to the left:

92-(4p(6p-3))=0


We calculate terms in parentheses: -(4p(6p-3)), so:

4p(6p-3)

We multiply parentheses

24p^2-12p

Back to the equation:

-(24p^2-12p)


We get rid of parentheses

-24p^2+12p+92=0

a = -24; b = 12; c = +92;
Δ = b2-4ac
Δ = 122-4·(-24)·92
Δ = 8976
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:

$\sqrt{\Delta}=\sqrt{8976}=\sqrt{16*561}=\sqrt{16}*\sqrt{561}=4\sqrt{561}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{561}}{2*-24}=\frac{-12-4\sqrt{561}}{-48}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{561}}{2*-24}=\frac{-12+4\sqrt{561}}{-48}
$