1/5x+x=-24

Solution for 1/5x+x=-24 equation:

1/5x+x=-24

We move all terms to the left:

1/5x+x-(-24)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/5x+24=0

We multiply all the terms by the denominator


x*5x+24*5x+1=0

Wy multiply elements

5x^2+120x+1=0

a = 5; b = 120; c = +1;
Δ = b2-4ac
Δ = 1202-4·5·1
Δ = 14380
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:

$\sqrt{\Delta}=\sqrt{14380}=\sqrt{4*3595}=\sqrt{4}*\sqrt{3595}=2\sqrt{3595}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-2\sqrt{3595}}{2*5}=\frac{-120-2\sqrt{3595}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+2\sqrt{3595}}{2*5}=\frac{-120+2\sqrt{3595}}{10}
$