Y=5x+1/9x-4

Solution for Y=5x+1/9x-4 equation:

=5Y+1/9Y-4

We move all terms to the left:

-(5Y+1/9Y-4)=0


Domain of the equation: 9Y-4)!=0

Y∈R


We get rid of parentheses

-5Y-1/9Y+4=0

We multiply all the terms by the denominator


-5Y*9Y+4*9Y-1=0

Wy multiply elements

-45Y^2+36Y-1=0

a = -45; b = 36; c = -1;
Δ = b2-4ac
Δ = 362-4·(-45)·(-1)
Δ = 1116
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:

$\sqrt{\Delta}=\sqrt{1116}=\sqrt{36*31}=\sqrt{36}*\sqrt{31}=6\sqrt{31}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{31}}{2*-45}=\frac{-36-6\sqrt{31}}{-90}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{31}}{2*-45}=\frac{-36+6\sqrt{31}}{-90}
$