x/13x+9=6x-12

Solution for x/13x+9=6x-12 equation:

x/13x+9=6x-12

We move all terms to the left:

x/13x+9-(6x-12)=0


Domain of the equation: 13x!=0

x!=0/13

x!=0

x∈R


We get rid of parentheses

x/13x-6x+12+9=0

We multiply all the terms by the denominator


x-6x*13x+12*13x+9*13x=0

Wy multiply elements

-78x^2+x+156x+117x=0

We add all the numbers together, and all the variables

-78x^2+274x=0

a = -78; b = 274; c = 0;
Δ = b2-4ac
Δ = 2742-4·(-78)·0
Δ = 75076
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{75076}=274$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(274)-274}{2*-78}=\frac{-548}{-156}
=3+20/39
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(274)+274}{2*-78}=\frac{0}{-156}
=0
$