3(2x+5)-22=3/x

Solution for 3(2x+5)-22=3/x equation:

3(2x+5)-22=3/x

We move all terms to the left:

3(2x+5)-22-(3/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

3(2x+5)-(+3/x)-22=0

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

6x^2-7x-3=0

a = 6; b = -7; c = -3;
Δ = b2-4ac
Δ = -72-4·6·(-3)
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*6}=\frac{-4}{12}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+11}{2*6}=\frac{18}{12}
=1+1/2
$