4x(9x+5)=3x

Solution for 4x(9x+5)=3x equation:

4x(9x+5)=3x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

36x^2-3x+20x=0

We add all the numbers together, and all the variables

36x^2+17x=0

a = 36; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·36·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*36}=\frac{-34}{72}
=-17/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*36}=\frac{0}{72}
=0
$