6-1p^2/8=-4

Solution for 6-1p^2/8=-4 equation:

6-1p^2/8=-4

We move all terms to the left:

6-1p^2/8-(-4)=0

We add all the numbers together, and all the variables

-1p^2/8+10=0

We multiply all the terms by the denominator


-1p^2+10*8=0

We add all the numbers together, and all the variables

-1p^2+80=0

a = -1; b = 0; c = +80;
Δ = b2-4ac
Δ = 02-4·(-1)·80
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{5}}{2*-1}=\frac{0-8\sqrt{5}}{-2}
=-\frac{8\sqrt{5}}{-2}
=-\frac{4\sqrt{5}}{-1}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{5}}{2*-1}=\frac{0+8\sqrt{5}}{-2}
=\frac{8\sqrt{5}}{-2}
=\frac{4\sqrt{5}}{-1}
$