(6/x-5)-5x=0

Solution for (6/x-5)-5x=0 equation:

(6/x-5)-5x=0


Domain of the equation: x-5)!=0

x∈R


We add all the numbers together, and all the variables

-5x+(6/x-5)=0

We get rid of parentheses

-5x+6/x-5=0

We multiply all the terms by the denominator


-5x*x-5*x+6=0

We add all the numbers together, and all the variables

-5x-5x*x+6=0

Wy multiply elements

-5x^2-5x+6=0

a = -5; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·(-5)·6
Δ = 145
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{-(-5)-\sqrt{145}}{2*-5}=\frac{5-\sqrt{145}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{145}}{2*-5}=\frac{5+\sqrt{145}}{-10}
$