4x=3/x+11

Solution for 4x=3/x+11 equation:

4x=3/x+11

We move all terms to the left:

4x-(3/x+11)=0


Domain of the equation: x+11)!=0

x∈R


We get rid of parentheses

4x-3/x-11=0

We multiply all the terms by the denominator


4x*x-11*x-3=0

We add all the numbers together, and all the variables

-11x+4x*x-3=0

Wy multiply elements

4x^2-11x-3=0

a = 4; b = -11; c = -3;
Δ = b2-4ac
Δ = -112-4·4·(-3)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-13}{2*4}=\frac{-2}{8}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+13}{2*4}=\frac{24}{8}
=3
$