3(x+9)=6x2

Solution for 3(x+9)=6x2 equation:

3(x+9)=6x^2

We move all terms to the left:

3(x+9)-(6x^2)=0

determiningTheFunctionDomain
-6x^2+3(x+9)=0

We multiply parentheses

-6x^2+3x+27=0

a = -6; b = 3; c = +27;
Δ = b2-4ac
Δ = 32-4·(-6)·27
Δ = 657
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:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{73}}{2*-6}=\frac{-3-3\sqrt{73}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{73}}{2*-6}=\frac{-3+3\sqrt{73}}{-12}
$