12x-15=6-7/3x

Solution for 12x-15=6-7/3x equation:

12x-15=6-7/3x

We move all terms to the left:

12x-15-(6-7/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

12x-(-7/3x+6)-15=0

We get rid of parentheses

12x+7/3x-6-15=0

We multiply all the terms by the denominator


12x*3x-6*3x-15*3x+7=0

Wy multiply elements

36x^2-18x-45x+7=0

We add all the numbers together, and all the variables

36x^2-63x+7=0

a = 36; b = -63; c = +7;
Δ = b2-4ac
Δ = -632-4·36·7
Δ = 2961
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:

$\sqrt{\Delta}=\sqrt{2961}=\sqrt{9*329}=\sqrt{9}*\sqrt{329}=3\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{329}}{2*36}=\frac{63-3\sqrt{329}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{329}}{2*36}=\frac{63+3\sqrt{329}}{72}
$