x-4/9x=5

Solution for x-4/9x=5 equation:

x-4/9x=5

We move all terms to the left:

x-4/9x-(5)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We multiply all the terms by the denominator


x*9x-5*9x-4=0

Wy multiply elements

9x^2-45x-4=0

a = 9; b = -45; c = -4;
Δ = b2-4ac
Δ = -452-4·9·(-4)
Δ = 2169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2169}=\sqrt{9*241}=\sqrt{9}*\sqrt{241}=3\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{241}}{2*9}=\frac{45-3\sqrt{241}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{241}}{2*9}=\frac{45+3\sqrt{241}}{18}
$