P=x^2/6-4

Solution for P=x^2/6-4 equation:

=P^2/6-4

We move all terms to the left:

-(P^2/6-4)=0

We get rid of parentheses

-P^2/6+4=0

We multiply all the terms by the denominator


-P^2+4*6=0

We add all the numbers together, and all the variables

-1P^2+24=0

a = -1; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-1)·24
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*-1}=\frac{0-4\sqrt{6}}{-2}
=-\frac{4\sqrt{6}}{-2}
=-\frac{2\sqrt{6}}{-1}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*-1}=\frac{0+4\sqrt{6}}{-2}
=\frac{4\sqrt{6}}{-2}
=\frac{2\sqrt{6}}{-1}
$