320/d2=6

Solution for 320/d2=6 equation:

320/d2=6

We move all terms to the left:

320/d2-(6)=0


Domain of the equation: d2!=0

d^2!=0/

d^2!=√0

d!=0

d∈R


We multiply all the terms by the denominator


-6*d2+320=0

We add all the numbers together, and all the variables

-6d^2+320=0

a = -6; b = 0; c = +320;
Δ = b2-4ac
Δ = 02-4·(-6)·320
Δ = 7680
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7680}=\sqrt{256*30}=\sqrt{256}*\sqrt{30}=16\sqrt{30}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{30}}{2*-6}=\frac{0-16\sqrt{30}}{-12}
=-\frac{16\sqrt{30}}{-12}
=-\frac{4\sqrt{30}}{-3}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{30}}{2*-6}=\frac{0+16\sqrt{30}}{-12}
=\frac{16\sqrt{30}}{-12}
=\frac{4\sqrt{30}}{-3}
$