2/3*d=109

Solution for 2/3*d=109 equation:

2/3*d=109

We move all terms to the left:

2/3*d-(109)=0


Domain of the equation: 3*d!=0

d!=0/1

d!=0

d∈R


We multiply all the terms by the denominator


-109*3*d+2=0

Wy multiply elements

-327d*d+2=0

Wy multiply elements

-327d^2+2=0

a = -327; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-327)·2
Δ = 2616
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:

$\sqrt{\Delta}=\sqrt{2616}=\sqrt{4*654}=\sqrt{4}*\sqrt{654}=2\sqrt{654}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{654}}{2*-327}=\frac{0-2\sqrt{654}}{-654}
=-\frac{2\sqrt{654}}{-654}
=-\frac{\sqrt{654}}{-327}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{654}}{2*-327}=\frac{0+2\sqrt{654}}{-654}
=\frac{2\sqrt{654}}{-654}
=\frac{\sqrt{654}}{-327}
$