1/5x+2=-x+8

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

1/5x+2=-x+8

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


1x*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}
$