0.666(x-6)=-1/3x-14

Solution for 0.666(x-6)=-1/3x-14 equation:

0.666(x-6)=-1/3x-14

We move all terms to the left:

0.666(x-6)-(-1/3x-14)=0


Domain of the equation: 3x-14)!=0

x∈R


We multiply parentheses

0.666x-(-1/3x-14)-3.996=0

We get rid of parentheses

0.666x+1/3x+14-3.996=0

We multiply all the terms by the denominator


(0.666x)*3x+14*3x-(3.996)*3x+1=0

We add all the numbers together, and all the variables

(+0.666x)*3x+14*3x-(3.996)*3x+1=0

We multiply parentheses

0x^2+14*3x-11.988x+1=0

Wy multiply elements

0x^2+42x-11.988x+1=0

We add all the numbers together, and all the variables

x^2+30.012x+1=0

a = 1; b = 30.012; c = +1;
Δ = b2-4ac
Δ = 30.0122-4·1·1
Δ = 896.720144
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{-(30.012)-\sqrt{896.720144}}{2*1}=\frac{-30.012-\sqrt{896.720144}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30.012)+\sqrt{896.720144}}{2*1}=\frac{-30.012+\sqrt{896.720144}}{2}
$