4x+8=25/x

Solution for 4x+8=25/x equation:

4x+8=25/x

We move all terms to the left:

4x+8-(25/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+25/x)+8=0

We get rid of parentheses

4x-25/x+8=0

We multiply all the terms by the denominator


4x*x+8*x-25=0

We add all the numbers together, and all the variables

8x+4x*x-25=0

Wy multiply elements

4x^2+8x-25=0

a = 4; b = 8; c = -25;
Δ = b2-4ac
Δ = 82-4·4·(-25)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{29}}{2*4}=\frac{-8-4\sqrt{29}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{29}}{2*4}=\frac{-8+4\sqrt{29}}{8}
$