4(p-2)7p=14

Solution for 4(p-2)7p=14 equation:

4(p-2)7p=14

We move all terms to the left:

4(p-2)7p-(14)=0

We multiply parentheses

28p^2-56p-14=0

a = 28; b = -56; c = -14;
Δ = b2-4ac
Δ = -562-4·28·(-14)
Δ = 4704
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:

$\sqrt{\Delta}=\sqrt{4704}=\sqrt{784*6}=\sqrt{784}*\sqrt{6}=28\sqrt{6}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-28\sqrt{6}}{2*28}=\frac{56-28\sqrt{6}}{56}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+28\sqrt{6}}{2*28}=\frac{56+28\sqrt{6}}{56}
$