0.8x+6=2/0.4x+3

Solution for 0.8x+6=2/0.4x+3 equation:

0.8x+6=2/0.4x+3

We move all terms to the left:

0.8x+6-(2/0.4x+3)=0


Domain of the equation: 0.4x+3)!=0

x∈R


We get rid of parentheses

0.8x-2/0.4x-3+6=0

We multiply all the terms by the denominator


(0.8x)*0.4x-3*0.4x+6*0.4x-2=0

We add all the numbers together, and all the variables

(+0.8x)*0.4x-3*0.4x+6*0.4x-2=0

We multiply parentheses

0x^2-3*0.4x+6*0.4x-2=0

Wy multiply elements

0x^2+0x+0x-2=0

We add all the numbers together, and all the variables

x^2+2x-2=0

a = 1; b = 2; c = -2;
Δ = b2-4ac
Δ = 22-4·1·(-2)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{3}}{2*1}=\frac{-2-2\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{3}}{2*1}=\frac{-2+2\sqrt{3}}{2}
$