2/5x-2=0.4x+12

Solution for 2/5x-2=0.4x+12 equation:

2/5x-2=0.4x+12

We move all terms to the left:

2/5x-2-(0.4x+12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-0.4x-12-2=0

We multiply all the terms by the denominator


-(0.4x)*5x-12*5x-2*5x+2=0

We add all the numbers together, and all the variables

-(+0.4x)*5x-12*5x-2*5x+2=0

We multiply parentheses

-0x^2-12*5x-2*5x+2=0

Wy multiply elements

-0x^2-60x-10x+2=0

We add all the numbers together, and all the variables

-1x^2-70x+2=0

a = -1; b = -70; c = +2;
Δ = b2-4ac
Δ = -702-4·(-1)·2
Δ = 4908
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:

$\sqrt{\Delta}=\sqrt{4908}=\sqrt{4*1227}=\sqrt{4}*\sqrt{1227}=2\sqrt{1227}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1227}}{2*-1}=\frac{70-2\sqrt{1227}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1227}}{2*-1}=\frac{70+2\sqrt{1227}}{-2}
$