2x+6=6x2

Solution for 2x+6=6x2 equation:

2x+6=6x^2

We move all terms to the left:

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

determiningTheFunctionDomain
-6x^2+2x+6=0

a = -6; b = 2; c = +6;
Δ = b2-4ac
Δ = 22-4·(-6)·6
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{37}}{2*-6}=\frac{-2-2\sqrt{37}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{37}}{2*-6}=\frac{-2+2\sqrt{37}}{-12}
$