13/x+4=3x+2

Solution for 13/x+4=3x+2 equation:

13/x+4=3x+2

We move all terms to the left:

13/x+4-(3x+2)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

13/x-3x-2+4=0

We multiply all the terms by the denominator


-3x*x-2*x+4*x+13=0

We add all the numbers together, and all the variables

2x-3x*x+13=0

Wy multiply elements

-3x^2+2x+13=0

a = -3; b = 2; c = +13;
Δ = b2-4ac
Δ = 22-4·(-3)·13
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{10}}{2*-3}=\frac{-2-4\sqrt{10}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{10}}{2*-3}=\frac{-2+4\sqrt{10}}{-6}
$