Y=x+4/x-7

Solution for Y=x+4/x-7 equation:

=Y+4/Y-7

We move all terms to the left:

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


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

Y∈R


We get rid of parentheses

-Y-4/Y+7=0

We multiply all the terms by the denominator


-Y*Y+7*Y-4=0

We add all the numbers together, and all the variables

7Y-Y*Y-4=0

Wy multiply elements

-1Y^2+7Y-4=0

a = -1; b = 7; c = -4;
Δ = b2-4ac
Δ = 72-4·(-1)·(-4)
Δ = 33
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{-(7)-\sqrt{33}}{2*-1}=\frac{-7-\sqrt{33}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{33}}{2*-1}=\frac{-7+\sqrt{33}}{-2}
$