5x-6+7=15/3x

Solution for 5x-6+7=15/3x equation:

5x-6+7=15/3x

We move all terms to the left:

5x-6+7-(15/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+15/3x)-6+7=0

We add all the numbers together, and all the variables

5x-(+15/3x)+1=0

We get rid of parentheses

5x-15/3x+1=0

We multiply all the terms by the denominator


5x*3x+1*3x-15=0

Wy multiply elements

15x^2+3x-15=0

a = 15; b = 3; c = -15;
Δ = b2-4ac
Δ = 32-4·15·(-15)
Δ = 909
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:

$\sqrt{\Delta}=\sqrt{909}=\sqrt{9*101}=\sqrt{9}*\sqrt{101}=3\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{101}}{2*15}=\frac{-3-3\sqrt{101}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{101}}{2*15}=\frac{-3+3\sqrt{101}}{30}
$