(37/9)v=17/18

Solution for (37/9)v=17/18 equation:

(37/9)v=17/18

We move all terms to the left:

(37/9)v-(17/18)=0


Domain of the equation: 9)v!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

(+37/9)v-(+17/18)=0

We multiply parentheses

37v^2-(+17/18)=0

We get rid of parentheses

37v^2-17/18=0

We multiply all the terms by the denominator


37v^2*18-17=0

Wy multiply elements

666v^2-17=0

a = 666; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·666·(-17)
Δ = 45288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{45288}=\sqrt{36*1258}=\sqrt{36}*\sqrt{1258}=6\sqrt{1258}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{1258}}{2*666}=\frac{0-6\sqrt{1258}}{1332}
=-\frac{6\sqrt{1258}}{1332}
=-\frac{\sqrt{1258}}{222}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{1258}}{2*666}=\frac{0+6\sqrt{1258}}{1332}
=\frac{6\sqrt{1258}}{1332}
=\frac{\sqrt{1258}}{222}
$