(107/6)y=38

Solution for (107/6)y=38 equation:

(107/6)y=38

We move all terms to the left:

(107/6)y-(38)=0


Domain of the equation: 6)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+107/6)y-38=0

We multiply parentheses

107y^2-38=0

a = 107; b = 0; c = -38;
Δ = b2-4ac
Δ = 02-4·107·(-38)
Δ = 16264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{16264}=\sqrt{4*4066}=\sqrt{4}*\sqrt{4066}=2\sqrt{4066}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{4066}}{2*107}=\frac{0-2\sqrt{4066}}{214}
=-\frac{2\sqrt{4066}}{214}
=-\frac{\sqrt{4066}}{107}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{4066}}{2*107}=\frac{0+2\sqrt{4066}}{214}
=\frac{2\sqrt{4066}}{214}
=\frac{\sqrt{4066}}{107}
$