4x+3=8/x

Solution for 4x+3=8/x equation:

4x+3=8/x

We move all terms to the left:

4x+3-(8/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-(+8/x)+3=0

We get rid of parentheses

4x-8/x+3=0

We multiply all the terms by the denominator


4x*x+3*x-8=0

We add all the numbers together, and all the variables

3x+4x*x-8=0

Wy multiply elements

4x^2+3x-8=0

a = 4; b = 3; c = -8;
Δ = b2-4ac
Δ = 32-4·4·(-8)
Δ = 137
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{-(3)-\sqrt{137}}{2*4}=\frac{-3-\sqrt{137}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{137}}{2*4}=\frac{-3+\sqrt{137}}{8}
$