3.50/r2.50=16

Solution for 3.50/r2.50=16 equation:

3.50/r2.50=16

We move all terms to the left:

3.50/r2.50-(16)=0


Domain of the equation: r2.50!=0

r!=0/1

r!=0

r∈R


We multiply all the terms by the denominator


-16*r2.50+3.50=0

We add all the numbers together, and all the variables

-16*r2.50+3.5=0

Wy multiply elements

-16r^2+3.5=0

a = -16; b = 0; c = +3.5;
Δ = b2-4ac
Δ = 02-4·(-16)·3.5
Δ = 224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{14}}{2*-16}=\frac{0-4\sqrt{14}}{-32}
=-\frac{4\sqrt{14}}{-32}
=-\frac{\sqrt{14}}{-8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{14}}{2*-16}=\frac{0+4\sqrt{14}}{-32}
=\frac{4\sqrt{14}}{-32}
=\frac{\sqrt{14}}{-8}
$