2/3x-1.6=8.8-2.9x

Solution for 2/3x-1.6=8.8-2.9x equation:

2/3x-1.6=8.8-2.9x

We move all terms to the left:

2/3x-1.6-(8.8-2.9x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(-2.9x+8.8)-1.6=0

We get rid of parentheses

2/3x+2.9x-8.8-1.6=0

We multiply all the terms by the denominator


(2.9x)*3x-(8.8)*3x-(1.6)*3x+2=0

We add all the numbers together, and all the variables

(+2.9x)*3x-(8.8)*3x-(1.6)*3x+2=0

We multiply parentheses

6x^2-26.4x-4.8x+2=0

We add all the numbers together, and all the variables

6x^2-31.2x+2=0

a = 6; b = -31.2; c = +2;
Δ = b2-4ac
Δ = -31.22-4·6·2
Δ = 925.44
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{-(-31.2)-\sqrt{925.44}}{2*6}=\frac{31.2-\sqrt{925.44}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31.2)+\sqrt{925.44}}{2*6}=\frac{31.2+\sqrt{925.44}}{12}
$