x-52.36/x=0.23

Solution for x-52.36/x=0.23 equation:

x-52.36/x=0.23

We move all terms to the left:

x-52.36/x-(0.23)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-52.36/x-0.23=0

We multiply all the terms by the denominator


x*x-(0.23)*x-52.36=0

We multiply parentheses

x*x-0.23x-52.36=0

Wy multiply elements

x^2-0.23x-52.36=0

a = 1; b = -0.23; c = -52.36;
Δ = b2-4ac
Δ = -0.232-4·1·(-52.36)
Δ = 209.4929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.23)-\sqrt{209.4929}}{2*1}=\frac{0.23-\sqrt{209.4929}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.23)+\sqrt{209.4929}}{2*1}=\frac{0.23+\sqrt{209.4929}}{2}
$