0,4(x+5)-3=2/5x-1

Solution for 0,4(x+5)-3=2/5x-1 equation:

0.4(x+5)-3=2/5x-1

We move all terms to the left:

0.4(x+5)-3-(2/5x-1)=0


Domain of the equation: 5x-1)!=0

x∈R


We multiply parentheses

0.4x-(2/5x-1)+2-3=0

We get rid of parentheses

0.4x-2/5x+1+2-3=0

We multiply all the terms by the denominator


(0.4x)*5x+1*5x+2*5x-3*5x-2=0

We add all the numbers together, and all the variables

(+0.4x)*5x+1*5x+2*5x-3*5x-2=0

We multiply parentheses

0x^2+1*5x+2*5x-3*5x-2=0

Wy multiply elements

0x^2+5x+10x-15x-2=0

We add all the numbers together, and all the variables

x^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}
=-\sqrt{2}
$
$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}
=\sqrt{2}
$