P(h)=-2/8h+4

Solution for P(h)=-2/8h+4 equation:

(P)=-2/8P+4

We move all terms to the left:

(P)-(-2/8P+4)=0


Domain of the equation: 8P+4)!=0

P∈R


We get rid of parentheses

P+2/8P-4=0

We multiply all the terms by the denominator


P*8P-4*8P+2=0

Wy multiply elements

8P^2-32P+2=0

a = 8; b = -32; c = +2;
Δ = b2-4ac
Δ = -322-4·8·2
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{15}}{2*8}=\frac{32-8\sqrt{15}}{16}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{15}}{2*8}=\frac{32+8\sqrt{15}}{16}
$