1/5x-4=42x+9

Solution for 1/5x-4=42x+9 equation:

1/5x-4=42x+9

We move all terms to the left:

1/5x-4-(42x+9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-42x-9-4=0

We multiply all the terms by the denominator


-42x*5x-9*5x-4*5x+1=0

Wy multiply elements

-210x^2-45x-20x+1=0

We add all the numbers together, and all the variables

-210x^2-65x+1=0

a = -210; b = -65; c = +1;
Δ = b2-4ac
Δ = -652-4·(-210)·1
Δ = 5065
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-\sqrt{5065}}{2*-210}=\frac{65-\sqrt{5065}}{-420}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{5065}}{2*-210}=\frac{65+\sqrt{5065}}{-420}
$