4/5x-1.4x=11

Solution for 4/5x-1.4x=11 equation:

4/5x-1.4x=11

We move all terms to the left:

4/5x-1.4x-(11)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1.4x+4/5x-11=0

We multiply all the terms by the denominator


-(1.4x)*5x-11*5x+4=0

We add all the numbers together, and all the variables

-(+1.4x)*5x-11*5x+4=0

We multiply parentheses

-5x^2-11*5x+4=0

Wy multiply elements

-5x^2-55x+4=0

a = -5; b = -55; c = +4;
Δ = b2-4ac
Δ = -552-4·(-5)·4
Δ = 3105
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:

$\sqrt{\Delta}=\sqrt{3105}=\sqrt{9*345}=\sqrt{9}*\sqrt{345}=3\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-3\sqrt{345}}{2*-5}=\frac{55-3\sqrt{345}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+3\sqrt{345}}{2*-5}=\frac{55+3\sqrt{345}}{-10}
$