3(x+5)=6/x+22

Solution for 3(x+5)=6/x+22 equation:

3(x+5)=6/x+22

We move all terms to the left:

3(x+5)-(6/x+22)=0


Domain of the equation: x+22)!=0

x∈R


We multiply parentheses

3x-(6/x+22)+15=0

We get rid of parentheses

3x-6/x-22+15=0

We multiply all the terms by the denominator


3x*x-22*x+15*x-6=0

We add all the numbers together, and all the variables

-7x+3x*x-6=0

Wy multiply elements

3x^2-7x-6=0

a = 3; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·3·(-6)
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{-(-7)-11}{2*3}=\frac{-4}{6}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+11}{2*3}=\frac{18}{6}
=3
$