4x(9x-3)=(2x+4)

Solution for 4x(9x-3)=(2x+4) equation:

4x(9x-3)=(2x+4)

We move all terms to the left:

4x(9x-3)-((2x+4))=0

We multiply parentheses

36x^2-12x-((2x+4))=0


We calculate terms in parentheses: -((2x+4)), so:

(2x+4)

We get rid of parentheses

2x+4

Back to the equation:

-(2x+4)


We get rid of parentheses

36x^2-12x-2x-4=0

We add all the numbers together, and all the variables

36x^2-14x-4=0

a = 36; b = -14; c = -4;
Δ = b2-4ac
Δ = -142-4·36·(-4)
Δ = 772
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{193}}{2*36}=\frac{14-2\sqrt{193}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{193}}{2*36}=\frac{14+2\sqrt{193}}{72}
$