4/x+6=x+3

Solution for 4/x+6=x+3 equation:

4/x+6=x+3

We move all terms to the left:

4/x+6-(x+3)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

4/x-x-3+6=0

We multiply all the terms by the denominator


-x*x-3*x+6*x+4=0

We add all the numbers together, and all the variables

3x-x*x+4=0

Wy multiply elements

-1x^2+3x+4=0

a = -1; b = 3; c = +4;
Δ = b2-4ac
Δ = 32-4·(-1)·4
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{-(3)-5}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5}{2*-1}=\frac{2}{-2}
=-1
$