4/5x-6=x+2

Solution for 4/5x-6=x+2 equation:

4/5x-6=x+2

We move all terms to the left:

4/5x-6-(x+2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-x-2-6=0

We multiply all the terms by the denominator


-x*5x-2*5x-6*5x+4=0

Wy multiply elements

-5x^2-10x-30x+4=0

We add all the numbers together, and all the variables

-5x^2-40x+4=0

a = -5; b = -40; c = +4;
Δ = b2-4ac
Δ = -402-4·(-5)·4
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{105}}{2*-5}=\frac{40-4\sqrt{105}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{105}}{2*-5}=\frac{40+4\sqrt{105}}{-10}
$