5x(6x+9)=1/6

Solution for 5x(6x+9)=1/6 equation:

5x(6x+9)=1/6

We move all terms to the left:

5x(6x+9)-(1/6)=0

We add all the numbers together, and all the variables

5x(6x+9)-(+1/6)=0

We multiply parentheses

30x^2+45x-(+1/6)=0

We get rid of parentheses

30x^2+45x-1/6=0

We multiply all the terms by the denominator


30x^2*6+45x*6-1=0

Wy multiply elements

180x^2+270x-1=0

a = 180; b = 270; c = -1;
Δ = b2-4ac
Δ = 2702-4·180·(-1)
Δ = 73620
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:

$\sqrt{\Delta}=\sqrt{73620}=\sqrt{36*2045}=\sqrt{36}*\sqrt{2045}=6\sqrt{2045}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(270)-6\sqrt{2045}}{2*180}=\frac{-270-6\sqrt{2045}}{360}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(270)+6\sqrt{2045}}{2*180}=\frac{-270+6\sqrt{2045}}{360}
$