5/x+4=5x-2

Solution for 5/x+4=5x-2 equation:

5/x+4=5x-2

We move all terms to the left:

5/x+4-(5x-2)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

5/x-5x+2+4=0

We multiply all the terms by the denominator


-5x*x+2*x+4*x+5=0

We add all the numbers together, and all the variables

6x-5x*x+5=0

Wy multiply elements

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

a = -5; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·(-5)·5
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{34}}{2*-5}=\frac{-6-2\sqrt{34}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{34}}{2*-5}=\frac{-6+2\sqrt{34}}{-10}
$