2/5x+5=8-x

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

2/5x+5=8-x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

5x^2-40x+25x+2=0

We add all the numbers together, and all the variables

5x^2-15x+2=0

a = 5; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·5·2
Δ = 185
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{-(-15)-\sqrt{185}}{2*5}=\frac{15-\sqrt{185}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{185}}{2*5}=\frac{15+\sqrt{185}}{10}
$