2/3x+1.6x-3.45=-0.7x

Solution for 2/3x+1.6x-3.45=-0.7x equation:

2/3x+1.6x-3.45=-0.7x

We move all terms to the left:

2/3x+1.6x-3.45-(-0.7x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1.6x+2/3x-(-0.7x)-3.45=0

We get rid of parentheses

1.6x+2/3x+0.7x-3.45=0

We multiply all the terms by the denominator


(1.6x)*3x+(0.7x)*3x-(3.45)*3x+2=0

We add all the numbers together, and all the variables

(+1.6x)*3x+(+0.7x)*3x-(3.45)*3x+2=0

We multiply parentheses

3x^2+0x^2-10.35x+2=0

We add all the numbers together, and all the variables

4x^2-10.35x+2=0

a = 4; b = -10.35; c = +2;
Δ = b2-4ac
Δ = -10.352-4·4·2
Δ = 75.1225
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{-(-10.35)-\sqrt{75.1225}}{2*4}=\frac{10.35-\sqrt{75.1225}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10.35)+\sqrt{75.1225}}{2*4}=\frac{10.35+\sqrt{75.1225}}{8}
$