Y+5x=6/x=-1.0.1

Solution for Y+5x=6/x=-1.0.1 equation:

+5Y=6/Y=-1.0.1

We move all terms to the left:

+5Y-(6/Y)=0


Domain of the equation: Y)!=0

Y!=0/1

Y!=0

Y∈R


We add all the numbers together, and all the variables

5Y-(+6/Y)=0

We get rid of parentheses

5Y-6/Y=0

We multiply all the terms by the denominator


5Y*Y-6=0

Wy multiply elements

5Y^2-6=0

a = 5; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·5·(-6)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*5}=\frac{0-2\sqrt{30}}{10}
=-\frac{2\sqrt{30}}{10}
=-\frac{\sqrt{30}}{5}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*5}=\frac{0+2\sqrt{30}}{10}
=\frac{2\sqrt{30}}{10}
=\frac{\sqrt{30}}{5}
$