4=y+7/y-7

Solution for 4=y+7/y-7 equation:

4=y+7/y-7

We move all terms to the left:

4-(y+7/y-7)=0


Domain of the equation: y-7)!=0

y∈R


We get rid of parentheses

-y-7/y+7+4=0

We multiply all the terms by the denominator


-y*y+7*y+4*y-7=0

We add all the numbers together, and all the variables

11y-y*y-7=0

Wy multiply elements

-1y^2+11y-7=0

a = -1; b = 11; c = -7;
Δ = b2-4ac
Δ = 112-4·(-1)·(-7)
Δ = 93
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{93}}{2*-1}=\frac{-11-\sqrt{93}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{93}}{2*-1}=\frac{-11+\sqrt{93}}{-2}
$