30-y-4/y=40

Solution for 30-y-4/y=40 equation:

30-y-4/y=40

We move all terms to the left:

30-y-4/y-(40)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

-1y-4/y-10=0

We multiply all the terms by the denominator


-1y*y-10*y-4=0

We add all the numbers together, and all the variables

-10y-1y*y-4=0

Wy multiply elements

-1y^2-10y-4=0

a = -1; b = -10; c = -4;
Δ = b2-4ac
Δ = -102-4·(-1)·(-4)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{21}}{2*-1}=\frac{10-2\sqrt{21}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{21}}{2*-1}=\frac{10+2\sqrt{21}}{-2}
$