9x(4x-1)/2x=15

Solution for 9x(4x-1)/2x=15 equation:

9x(4x-1)/2x=15

We move all terms to the left:

9x(4x-1)/2x-(15)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


9x(4x-1)-15*2x=0

We multiply parentheses

36x^2-9x-15*2x=0

Wy multiply elements

36x^2-9x-30x=0

We add all the numbers together, and all the variables

36x^2-39x=0

a = 36; b = -39; c = 0;
Δ = b2-4ac
Δ = -392-4·36·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-39}{2*36}=\frac{0}{72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+39}{2*36}=\frac{78}{72}
=1+1/12
$