4x-7=5x+6/x

Solution for 4x-7=5x+6/x equation:

4x-7=5x+6/x

We move all terms to the left:

4x-7-(5x+6/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-(+5x+6/x)-7=0

We get rid of parentheses

4x-5x-6/x-7=0

We multiply all the terms by the denominator


4x*x-5x*x-7*x-6=0

We add all the numbers together, and all the variables

-7x+4x*x-5x*x-6=0

Wy multiply elements

4x^2-5x^2-7x-6=0

We add all the numbers together, and all the variables

-1x^2-7x-6=0

a = -1; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·(-1)·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*-1}=\frac{2}{-2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*-1}=\frac{12}{-2}
=-6
$