4p^2-4p=9

Solution for 4p^2-4p=9 equation:

4p^2-4p=9

We move all terms to the left:

4p^2-4p-(9)=0

a = 4; b = -4; c = -9;
Δ = b2-4ac
Δ = -42-4·4·(-9)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{10}}{2*4}=\frac{4-4\sqrt{10}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{10}}{2*4}=\frac{4+4\sqrt{10}}{8}
$