3/5x+8=-x

Solution for 3/5x+8=-x equation:

3/5x+8=-x

We move all terms to the left:

3/5x+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

3/5x-(-1x)+8=0

We get rid of parentheses

3/5x+1x+8=0

We multiply all the terms by the denominator


1x*5x+8*5x+3=0

Wy multiply elements

5x^2+40x+3=0

a = 5; b = 40; c = +3;
Δ = b2-4ac
Δ = 402-4·5·3
Δ = 1540
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:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{385}}{2*5}=\frac{-40-2\sqrt{385}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{385}}{2*5}=\frac{-40+2\sqrt{385}}{10}
$