-11/5x-7=0.4x+1

Solution for -11/5x-7=0.4x+1 equation:

-11/5x-7=0.4x+1

We move all terms to the left:

-11/5x-7-(0.4x+1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-11/5x-0.4x-1-7=0

We multiply all the terms by the denominator


-(0.4x)*5x-1*5x-7*5x-11=0

We add all the numbers together, and all the variables

-(+0.4x)*5x-1*5x-7*5x-11=0

We multiply parentheses

-0x^2-1*5x-7*5x-11=0

Wy multiply elements

-0x^2-5x-35x-11=0

We add all the numbers together, and all the variables

-1x^2-40x-11=0

a = -1; b = -40; c = -11;
Δ = b2-4ac
Δ = -402-4·(-1)·(-11)
Δ = 1556
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:

$\sqrt{\Delta}=\sqrt{1556}=\sqrt{4*389}=\sqrt{4}*\sqrt{389}=2\sqrt{389}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{389}}{2*-1}=\frac{40-2\sqrt{389}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{389}}{2*-1}=\frac{40+2\sqrt{389}}{-2}
$