1/3x-9=14x-7-13

Solution for 1/3x-9=14x-7-13 equation:

1/3x-9=14x-7-13

We move all terms to the left:

1/3x-9-(14x-7-13)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(14x-20)-9=0

We get rid of parentheses

1/3x-14x+20-9=0

We multiply all the terms by the denominator


-14x*3x+20*3x-9*3x+1=0

Wy multiply elements

-42x^2+60x-27x+1=0

We add all the numbers together, and all the variables

-42x^2+33x+1=0

a = -42; b = 33; c = +1;
Δ = b2-4ac
Δ = 332-4·(-42)·1
Δ = 1257
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{-(33)-\sqrt{1257}}{2*-42}=\frac{-33-\sqrt{1257}}{-84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1257}}{2*-42}=\frac{-33+\sqrt{1257}}{-84}
$