4=6x-15/x

Solution for 4=6x-15/x equation:

4=6x-15/x

We move all terms to the left:

4-(6x-15/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

-(+6x-15/x)+4=0

We get rid of parentheses

-6x+15/x+4=0

We multiply all the terms by the denominator


-6x*x+4*x+15=0

We add all the numbers together, and all the variables

4x-6x*x+15=0

Wy multiply elements

-6x^2+4x+15=0

a = -6; b = 4; c = +15;
Δ = b2-4ac
Δ = 42-4·(-6)·15
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{94}}{2*-6}=\frac{-4-2\sqrt{94}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{94}}{2*-6}=\frac{-4+2\sqrt{94}}{-12}
$