1/5x-10=-5x

Solution for 1/5x-10=-5x equation:

1/5x-10=-5x

We move all terms to the left:

1/5x-10-(-5x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x+5x-10=0

We multiply all the terms by the denominator


5x*5x-10*5x+1=0

Wy multiply elements

25x^2-50x+1=0

a = 25; b = -50; c = +1;
Δ = b2-4ac
Δ = -502-4·25·1
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-20\sqrt{6}}{2*25}=\frac{50-20\sqrt{6}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+20\sqrt{6}}{2*25}=\frac{50+20\sqrt{6}}{50}
$