-(4/5)x+14/5=x+2

Solution for -(4/5)x+14/5=x+2 equation:

-(4/5)x+14/5=x+2

We move all terms to the left:

-(4/5)x+14/5-(x+2)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+4/5)x-(x+2)+14/5=0

We multiply parentheses

-4x^2-(x+2)+14/5=0

We get rid of parentheses

-4x^2-x-2+14/5=0

We multiply all the terms by the denominator


-4x^2*5-x*5+14-2*5=0

We add all the numbers together, and all the variables

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

Wy multiply elements

-20x^2-5x+4=0

a = -20; b = -5; c = +4;
Δ = b2-4ac
Δ = -52-4·(-20)·4
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{345}}{2*-20}=\frac{5-\sqrt{345}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{345}}{2*-20}=\frac{5+\sqrt{345}}{-40}
$