12x-15=6-5/7x

Solution for 12x-15=6-5/7x equation:

12x-15=6-5/7x

We move all terms to the left:

12x-15-(6-5/7x)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

12x-(-5/7x+6)-15=0

We get rid of parentheses

12x+5/7x-6-15=0

We multiply all the terms by the denominator


12x*7x-6*7x-15*7x+5=0

Wy multiply elements

84x^2-42x-105x+5=0

We add all the numbers together, and all the variables

84x^2-147x+5=0

a = 84; b = -147; c = +5;
Δ = b2-4ac
Δ = -1472-4·84·5
Δ = 19929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-147)-\sqrt{19929}}{2*84}=\frac{147-\sqrt{19929}}{168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-147)+\sqrt{19929}}{2*84}=\frac{147+\sqrt{19929}}{168}
$