x+.75/x=18.75

Solution for x+.75/x=18.75 equation:

x+.75/x=18.75

We move all terms to the left:

x+.75/x-(18.75)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+.75/x-18.75=0

We multiply all the terms by the denominator


x*x-(18.75)*x+.75=0

We add all the numbers together, and all the variables

x*x-(18.75)*x+0.75=0

We multiply parentheses

x*x-18.75x+0.75=0

Wy multiply elements

x^2-18.75x+0.75=0

a = 1; b = -18.75; c = +0.75;
Δ = b2-4ac
Δ = -18.752-4·1·0.75
Δ = 348.5625
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{-(-18.75)-\sqrt{348.5625}}{2*1}=\frac{18.75-\sqrt{348.5625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18.75)+\sqrt{348.5625}}{2*1}=\frac{18.75+\sqrt{348.5625}}{2}
$