1/5x-1.6=x-16

Solution for 1/5x-1.6=x-16 equation:

1/5x-1.6=x-16

We move all terms to the left:

1/5x-1.6-(x-16)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-x+16-1.6=0

We multiply all the terms by the denominator


-x*5x+16*5x-(1.6)*5x+1=0

We multiply parentheses

-x*5x+16*5x-8x+1=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-5x^2+72x+1=0

a = -5; b = 72; c = +1;
Δ = b2-4ac
Δ = 722-4·(-5)·1
Δ = 5204
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:

$\sqrt{\Delta}=\sqrt{5204}=\sqrt{4*1301}=\sqrt{4}*\sqrt{1301}=2\sqrt{1301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-2\sqrt{1301}}{2*-5}=\frac{-72-2\sqrt{1301}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+2\sqrt{1301}}{2*-5}=\frac{-72+2\sqrt{1301}}{-10}
$