x-100/x=0.45

Solution for x-100/x=0.45 equation:

x-100/x=0.45

We move all terms to the left:

x-100/x-(0.45)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-100/x-0.45=0

We multiply all the terms by the denominator


x*x-(0.45)*x-100=0

We multiply parentheses

x*x-0.45x-100=0

Wy multiply elements

x^2-0.45x-100=0

a = 1; b = -0.45; c = -100;
Δ = b2-4ac
Δ = -0.452-4·1·(-100)
Δ = 400.2025
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{-(-0.45)-\sqrt{400.2025}}{2*1}=\frac{0.45-\sqrt{400.2025}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.45)+\sqrt{400.2025}}{2*1}=\frac{0.45+\sqrt{400.2025}}{2}
$