12/x+3=2x+8

Solution for 12/x+3=2x+8 equation:

12/x+3=2x+8

We move all terms to the left:

12/x+3-(2x+8)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

12/x-2x-8+3=0

We multiply all the terms by the denominator


-2x*x-8*x+3*x+12=0

We add all the numbers together, and all the variables

-5x-2x*x+12=0

Wy multiply elements

-2x^2-5x+12=0

a = -2; b = -5; c = +12;
Δ = b2-4ac
Δ = -52-4·(-2)·12
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*-2}=\frac{16}{-4}
=-4
$