6x+12=(4x)2

Solution for 6x+12=(4x)2 equation:

6x+12=(4x)2

We move all terms to the left:

6x+12-((4x)2)=0

determiningTheFunctionDomain
6x-4x2+12=0

We add all the numbers together, and all the variables

-4x^2+6x+12=0

a = -4; b = 6; c = +12;
Δ = b2-4ac
Δ = 62-4·(-4)·12
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{57}}{2*-4}=\frac{-6-2\sqrt{57}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{57}}{2*-4}=\frac{-6+2\sqrt{57}}{-8}
$