21=p^2-p/2

Solution for 21=p^2-p/2 equation:

21=p^2-p/2

We move all terms to the left:

21-(p^2-p/2)=0

We get rid of parentheses

-p^2+p/2+21=0

We multiply all the terms by the denominator


-p^2*2+p+21*2=0

We add all the numbers together, and all the variables

-p^2*2+p+42=0

Wy multiply elements

-2p^2+p+42=0

a = -2; b = 1; c = +42;
Δ = b2-4ac
Δ = 12-4·(-2)·42
Δ = 337
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{337}}{2*-2}=\frac{-1-\sqrt{337}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{337}}{2*-2}=\frac{-1+\sqrt{337}}{-4}
$