2/5x+12=0.4x+12

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

2/5x+12=0.4x+12

We move all terms to the left:

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

Wy multiply elements

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

We add all the numbers together, and all the variables

-1x^2+2=0

a = -1; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-1)·2
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2}}{2*-1}=\frac{0-2\sqrt{2}}{-2}
=-\frac{2\sqrt{2}}{-2}
=-\frac{\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2}}{2*-1}=\frac{0+2\sqrt{2}}{-2}
=\frac{2\sqrt{2}}{-2}
=\frac{\sqrt{2}}{-1}
$