x=75/x-10

Solution for x=75/x-10 equation:

x=75/x-10

We move all terms to the left:

x-(75/x-10)=0


Domain of the equation: x-10)!=0

x∈R


We get rid of parentheses

x-75/x+10=0

We multiply all the terms by the denominator


x*x+10*x-75=0

We add all the numbers together, and all the variables

10x+x*x-75=0

Wy multiply elements

x^2+10x-75=0

a = 1; b = 10; c = -75;
Δ = b2-4ac
Δ = 102-4·1·(-75)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-20}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+20}{2*1}=\frac{10}{2}
=5
$