1/5x-80=2x-8

Solution for 1/5x-80=2x-8 equation:

1/5x-80=2x-8

We move all terms to the left:

1/5x-80-(2x-8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-2x+8-80=0

We multiply all the terms by the denominator


-2x*5x+8*5x-80*5x+1=0

Wy multiply elements

-10x^2+40x-400x+1=0

We add all the numbers together, and all the variables

-10x^2-360x+1=0

a = -10; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·(-10)·1
Δ = 129640
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:

$\sqrt{\Delta}=\sqrt{129640}=\sqrt{4*32410}=\sqrt{4}*\sqrt{32410}=2\sqrt{32410}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-2\sqrt{32410}}{2*-10}=\frac{360-2\sqrt{32410}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+2\sqrt{32410}}{2*-10}=\frac{360+2\sqrt{32410}}{-20}
$