x/5x-4(x+3)=8

Solution for x/5x-4(x+3)=8 equation:

x/5x-4(x+3)=8

We move all terms to the left:

x/5x-4(x+3)-(8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply parentheses

x/5x-4x-12-8=0

We multiply all the terms by the denominator


x-4x*5x-12*5x-8*5x=0

Wy multiply elements

-20x^2+x-60x-40x=0

We add all the numbers together, and all the variables

-20x^2-99x=0

a = -20; b = -99; c = 0;
Δ = b2-4ac
Δ = -992-4·(-20)·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-99}{2*-20}=\frac{0}{-40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+99}{2*-20}=\frac{198}{-40}
=-4+19/20
$