4/x=4x+15

Solution for 4/x=4x+15 equation:

4/x=4x+15

We move all terms to the left:

4/x-(4x+15)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

4/x-4x-15=0

We multiply all the terms by the denominator


-4x*x-15*x+4=0

We add all the numbers together, and all the variables

-15x-4x*x+4=0

Wy multiply elements

-4x^2-15x+4=0

a = -4; b = -15; c = +4;
Δ = b2-4ac
Δ = -152-4·(-4)·4
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-17}{2*-4}=\frac{-2}{-8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+17}{2*-4}=\frac{32}{-8}
=-4
$