4p(2+2.50)p=31.50

Solution for 4p(2+2.50)p=31.50 equation:

4p(2+2.50)p=31.50

We move all terms to the left:

4p(2+2.50)p-(31.50)=0

We add all the numbers together, and all the variables

4p(4.5)p-(31.5)=0

We add all the numbers together, and all the variables

4p(4.5)p-31.5=0

We multiply parentheses

18p^2-31.5=0

a = 18; b = 0; c = -31.5;
Δ = b2-4ac
Δ = 02-4·18·(-31.5)
Δ = 2268
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:

$\sqrt{\Delta}=\sqrt{2268}=\sqrt{324*7}=\sqrt{324}*\sqrt{7}=18\sqrt{7}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{7}}{2*18}=\frac{0-18\sqrt{7}}{36}
=-\frac{18\sqrt{7}}{36}
=-\frac{\sqrt{7}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{7}}{2*18}=\frac{0+18\sqrt{7}}{36}
=\frac{18\sqrt{7}}{36}
=\frac{\sqrt{7}}{2}
$