1/5x-60=2x-6

Solution for 1/5x-60=2x-6 equation:

1/5x-60=2x-6

We move all terms to the left:

1/5x-60-(2x-6)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-2x+6-60=0

We multiply all the terms by the denominator


-2x*5x+6*5x-60*5x+1=0

Wy multiply elements

-10x^2+30x-300x+1=0

We add all the numbers together, and all the variables

-10x^2-270x+1=0

a = -10; b = -270; c = +1;
Δ = b2-4ac
Δ = -2702-4·(-10)·1
Δ = 72940
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:

$\sqrt{\Delta}=\sqrt{72940}=\sqrt{4*18235}=\sqrt{4}*\sqrt{18235}=2\sqrt{18235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-2\sqrt{18235}}{2*-10}=\frac{270-2\sqrt{18235}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+2\sqrt{18235}}{2*-10}=\frac{270+2\sqrt{18235}}{-20}
$