x/5x-6=4x+9

Solution for x/5x-6=4x+9 equation:

x/5x-6=4x+9

We move all terms to the left:

x/5x-6-(4x+9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

x/5x-4x-9-6=0

We multiply all the terms by the denominator


x-4x*5x-9*5x-6*5x=0

Wy multiply elements

-20x^2+x-45x-30x=0

We add all the numbers together, and all the variables

-20x^2-74x=0

a = -20; b = -74; c = 0;
Δ = b2-4ac
Δ = -742-4·(-20)·0
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-74}{2*-20}=\frac{0}{-40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+74}{2*-20}=\frac{148}{-40}
=-3+7/10
$