125x-0.25/x=7.5

Solution for 125x-0.25/x=7.5 equation:

125x-0.25/x=7.5

We move all terms to the left:

125x-0.25/x-(7.5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

125x-0.25/x-7.5=0

We multiply all the terms by the denominator


125x*x-(7.5)*x-0.25=0

We multiply parentheses

125x*x-7.5x-0.25=0

Wy multiply elements

125x^2-7.5x-0.25=0

a = 125; b = -7.5; c = -0.25;
Δ = b2-4ac
Δ = -7.52-4·125·(-0.25)
Δ = 181.25
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{-(-7.5)-\sqrt{181.25}}{2*125}=\frac{7.5-\sqrt{181.25}}{250}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.5)+\sqrt{181.25}}{2*125}=\frac{7.5+\sqrt{181.25}}{250}
$