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

Solution for 0.66(x-6)=-1/3x-14 equation:

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

We move all terms to the left:

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


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

x∈R


We multiply parentheses

0.66x-(-1/3x-14)-3.96=0

We get rid of parentheses

0.66x+1/3x+14-3.96=0

We multiply all the terms by the denominator


(0.66x)*3x+14*3x-(3.96)*3x+1=0

We add all the numbers together, and all the variables

(+0.66x)*3x+14*3x-(3.96)*3x+1=0

We multiply parentheses

0x^2+14*3x-11.88x+1=0

Wy multiply elements

0x^2+42x-11.88x+1=0

We add all the numbers together, and all the variables

x^2+30.12x+1=0

a = 1; b = 30.12; c = +1;
Δ = b2-4ac
Δ = 30.122-4·1·1
Δ = 903.2144
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{-(30.12)-\sqrt{903.2144}}{2*1}=\frac{-30.12-\sqrt{903.2144}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30.12)+\sqrt{903.2144}}{2*1}=\frac{-30.12+\sqrt{903.2144}}{2}
$