x-2=-1/5x-8

Solution for x-2=-1/5x-8 equation:

x-2=-1/5x-8

We move all terms to the left:

x-2-(-1/5x-8)=0


Domain of the equation: 5x-8)!=0

x∈R


We get rid of parentheses

x+1/5x+8-2=0

We multiply all the terms by the denominator


x*5x+8*5x-2*5x+1=0

Wy multiply elements

5x^2+40x-10x+1=0

We add all the numbers together, and all the variables

5x^2+30x+1=0

a = 5; b = 30; c = +1;
Δ = b2-4ac
Δ = 302-4·5·1
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-4\sqrt{55}}{2*5}=\frac{-30-4\sqrt{55}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+4\sqrt{55}}{2*5}=\frac{-30+4\sqrt{55}}{10}
$