-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 = 129560
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:

$\sqrt{\Delta}=\sqrt{129560}=\sqrt{4*32390}=\sqrt{4}*\sqrt{32390}=2\sqrt{32390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-2\sqrt{32390}}{2*-10}=\frac{-360-2\sqrt{32390}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+2\sqrt{32390}}{2*-10}=\frac{-360+2\sqrt{32390}}{-20}
$