15000/q-0.25q=0

Solution for 15000/q-0.25q=0 equation:

15000/q-0.25q=0


Domain of the equation: q!=0

q∈R


We add all the numbers together, and all the variables

-0.25q+15000/q=0

We multiply all the terms by the denominator


-(0.25q)*q+15000=0

We add all the numbers together, and all the variables

-(+0.25q)*q+15000=0

We multiply parentheses

-0q^2+15000=0

We add all the numbers together, and all the variables

-1q^2+15000=0

a = -1; b = 0; c = +15000;
Δ = b2-4ac
Δ = 02-4·(-1)·15000
Δ = 60000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60000}=\sqrt{10000*6}=\sqrt{10000}*\sqrt{6}=100\sqrt{6}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{6}}{2*-1}=\frac{0-100\sqrt{6}}{-2}
=-\frac{100\sqrt{6}}{-2}
=-\frac{50\sqrt{6}}{-1}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{6}}{2*-1}=\frac{0+100\sqrt{6}}{-2}
=\frac{100\sqrt{6}}{-2}
=\frac{50\sqrt{6}}{-1}
$