5/9*x=65

Solution for 5/9*x=65 equation:

5/9*x=65

We move all terms to the left:

5/9*x-(65)=0


Domain of the equation: 9*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-65*9*x+5=0

Wy multiply elements

-585x*x+5=0

Wy multiply elements

-585x^2+5=0

a = -585; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-585)·5
Δ = 11700
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:

$\sqrt{\Delta}=\sqrt{11700}=\sqrt{900*13}=\sqrt{900}*\sqrt{13}=30\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{13}}{2*-585}=\frac{0-30\sqrt{13}}{-1170}
=-\frac{30\sqrt{13}}{-1170}
=-\frac{\sqrt{13}}{-39}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{13}}{2*-585}=\frac{0+30\sqrt{13}}{-1170}
=\frac{30\sqrt{13}}{-1170}
=\frac{\sqrt{13}}{-39}
$