x/4x-3=5x+9

Solution for x/4x-3=5x+9 equation:

x/4x-3=5x+9

We move all terms to the left:

x/4x-3-(5x+9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

x/4x-5x-9-3=0

We multiply all the terms by the denominator


x-5x*4x-9*4x-3*4x=0

Wy multiply elements

-20x^2+x-36x-12x=0

We add all the numbers together, and all the variables

-20x^2-47x=0

a = -20; b = -47; c = 0;
Δ = b2-4ac
Δ = -472-4·(-20)·0
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-47}{2*-20}=\frac{0}{-40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+47}{2*-20}=\frac{94}{-40}
=-2+7/20
$