1/3x-2(1/3x+5)=12

Solution for 1/3x-2(1/3x+5)=12 equation:

1/3x-2(1/3x+5)=12

We move all terms to the left:

1/3x-2(1/3x+5)-(12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x+5)!=0

x∈R


We multiply parentheses

1/3x-2x-10-12=0

We multiply all the terms by the denominator


-2x*3x-10*3x-12*3x+1=0

Wy multiply elements

-6x^2-30x-36x+1=0

We add all the numbers together, and all the variables

-6x^2-66x+1=0

a = -6; b = -66; c = +1;
Δ = b2-4ac
Δ = -662-4·(-6)·1
Δ = 4380
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:

$\sqrt{\Delta}=\sqrt{4380}=\sqrt{4*1095}=\sqrt{4}*\sqrt{1095}=2\sqrt{1095}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1095}}{2*-6}=\frac{66-2\sqrt{1095}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1095}}{2*-6}=\frac{66+2\sqrt{1095}}{-12}
$