P(x)=3/4x

Solution for P(x)=3/4x equation:

(P)=3/4P

We move all terms to the left:

(P)-(3/4P)=0


Domain of the equation: 4P)!=0

P!=0/1

P!=0

P∈R


We add all the numbers together, and all the variables

P-(+3/4P)=0

We get rid of parentheses

P-3/4P=0

We multiply all the terms by the denominator


P*4P-3=0

Wy multiply elements

4P^2-3=0

a = 4; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·4·(-3)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*4}=\frac{0-4\sqrt{3}}{8}
=-\frac{4\sqrt{3}}{8}
=-\frac{\sqrt{3}}{2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*4}=\frac{0+4\sqrt{3}}{8}
=\frac{4\sqrt{3}}{8}
=\frac{\sqrt{3}}{2}
$