1/5x=10x-120

Solution for 1/5x=10x-120 equation:

1/5x=10x-120

We move all terms to the left:

1/5x-(10x-120)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-10x+120=0

We multiply all the terms by the denominator


-10x*5x+120*5x+1=0

Wy multiply elements

-50x^2+600x+1=0

a = -50; b = 600; c = +1;
Δ = b2-4ac
Δ = 6002-4·(-50)·1
Δ = 360200
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:

$\sqrt{\Delta}=\sqrt{360200}=\sqrt{100*3602}=\sqrt{100}*\sqrt{3602}=10\sqrt{3602}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(600)-10\sqrt{3602}}{2*-50}=\frac{-600-10\sqrt{3602}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(600)+10\sqrt{3602}}{2*-50}=\frac{-600+10\sqrt{3602}}{-100}
$