Y=x+3/x-8

Solution for Y=x+3/x-8 equation:

=Y+3/Y-8

We move all terms to the left:

-(Y+3/Y-8)=0


Domain of the equation: Y-8)!=0

Y∈R


We get rid of parentheses

-Y-3/Y+8=0

We multiply all the terms by the denominator


-Y*Y+8*Y-3=0

We add all the numbers together, and all the variables

8Y-Y*Y-3=0

Wy multiply elements

-1Y^2+8Y-3=0

a = -1; b = 8; c = -3;
Δ = b2-4ac
Δ = 82-4·(-1)·(-3)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{13}}{2*-1}=\frac{-8-2\sqrt{13}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{13}}{2*-1}=\frac{-8+2\sqrt{13}}{-2}
$