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7/y=0.4y=
We move all terms to the left:
7/y-(0.4y)=0
Domain of the equation: y!=0We add all the numbers together, and all the variables
y∈R
7/y-(+0.4y)=0
We get rid of parentheses
7/y-0.4y=0
We multiply all the terms by the denominator
-(0.4y)*y+7=0
We add all the numbers together, and all the variables
-(+0.4y)*y+7=0
We multiply parentheses
-0y^2+7=0
We add all the numbers together, and all the variables
-1y^2+7=0
a = -1; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-1)·7
Δ = 28
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{7}}{2*-1}=\frac{0-2\sqrt{7}}{-2} =-\frac{2\sqrt{7}}{-2} =-\frac{\sqrt{7}}{-1} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{7}}{2*-1}=\frac{0+2\sqrt{7}}{-2} =\frac{2\sqrt{7}}{-2} =\frac{\sqrt{7}}{-1} $
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