5/9*x=45

Solution for 5/9*x=45 equation:

5/9*x=45

We move all terms to the left:

5/9*x-(45)=0


Domain of the equation: 9*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-45*9*x+5=0

Wy multiply elements

-405x*x+5=0

Wy multiply elements

-405x^2+5=0

a = -405; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-405)·5
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-90}{2*-405}=\frac{-90}{-810}
=1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+90}{2*-405}=\frac{90}{-810}
=-1/9
$