300p-13500/300p=0.30

Solution for 300p-13500/300p=0.30 equation:

300p-13500/300p=0.30

We move all terms to the left:

300p-13500/300p-(0.30)=0


Domain of the equation: 300p!=0

p!=0/300

p!=0

p∈R


We add all the numbers together, and all the variables

300p-13500/300p-(0.3)=0

We add all the numbers together, and all the variables

300p-13500/300p-0.3=0

We multiply all the terms by the denominator


300p*300p-(0.3)*300p-13500=0

We multiply parentheses

300p*300p-90p-13500=0

Wy multiply elements

90000p^2-90p-13500=0

a = 90000; b = -90; c = -13500;
Δ = b2-4ac
Δ = -902-4·90000·(-13500)
Δ = 4860008100
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:

$\sqrt{\Delta}=\sqrt{4860008100}=\sqrt{8100*600001}=\sqrt{8100}*\sqrt{600001}=90\sqrt{600001}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-90\sqrt{600001}}{2*90000}=\frac{90-90\sqrt{600001}}{180000}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90\sqrt{600001}}{2*90000}=\frac{90+90\sqrt{600001}}{180000}
$