9/13*x=1

Solution for 9/13*x=1 equation:

9/13*x=1

We move all terms to the left:

9/13*x-(1)=0


Domain of the equation: 13*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-1*13*x+9=0

Wy multiply elements

-13x*x+9=0

Wy multiply elements

-13x^2+9=0

a = -13; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-13)·9
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{13}}{2*-13}=\frac{0-6\sqrt{13}}{-26}
=-\frac{6\sqrt{13}}{-26}
=-\frac{3\sqrt{13}}{-13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{13}}{2*-13}=\frac{0+6\sqrt{13}}{-26}
=\frac{6\sqrt{13}}{-26}
=\frac{3\sqrt{13}}{-13}
$