18(20x+4)=3x(9x+6)

Solution for 18(20x+4)=3x(9x+6) equation:

18(20x+4)=3x(9x+6)

We move all terms to the left:

18(20x+4)-(3x(9x+6))=0

We multiply parentheses

360x-(3x(9x+6))+72=0


We calculate terms in parentheses: -(3x(9x+6)), so:

3x(9x+6)

We multiply parentheses

27x^2+18x

Back to the equation:

-(27x^2+18x)


We get rid of parentheses

-27x^2+360x-18x+72=0

We add all the numbers together, and all the variables

-27x^2+342x+72=0

a = -27; b = 342; c = +72;
Δ = b2-4ac
Δ = 3422-4·(-27)·72
Δ = 124740
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:

$\sqrt{\Delta}=\sqrt{124740}=\sqrt{324*385}=\sqrt{324}*\sqrt{385}=18\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(342)-18\sqrt{385}}{2*-27}=\frac{-342-18\sqrt{385}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(342)+18\sqrt{385}}{2*-27}=\frac{-342+18\sqrt{385}}{-54}
$