133/x*5+3(x-4)=2019

Solution for 133/x*5+3(x-4)=2019 equation:

133/x*5+3(x-4)=2019

We move all terms to the left:

133/x*5+3(x-4)-(2019)=0


Domain of the equation: x*5!=0

x!=0/1

x!=0

x∈R


We multiply parentheses

133/x*5+3x-12-2019=0

We multiply all the terms by the denominator


3x*x*5-12*x*5-2019*x*5+133=0

Wy multiply elements

15x^2*5-60x*5-10095x*5+133=0

Wy multiply elements

75x^2-300x-50475x+133=0

We add all the numbers together, and all the variables

75x^2-50775x+133=0

a = 75; b = -50775; c = +133;
Δ = b2-4ac
Δ = -507752-4·75·133
Δ = 2578060725
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:

$\sqrt{\Delta}=\sqrt{2578060725}=\sqrt{25*103122429}=\sqrt{25}*\sqrt{103122429}=5\sqrt{103122429}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50775)-5\sqrt{103122429}}{2*75}=\frac{50775-5\sqrt{103122429}}{150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50775)+5\sqrt{103122429}}{2*75}=\frac{50775+5\sqrt{103122429}}{150}
$