4x+16=(6x)2

Solution for 4x+16=(6x)2 equation:

4x+16=(6x)2

We move all terms to the left:

4x+16-((6x)2)=0

determiningTheFunctionDomain
4x-6x2+16=0

We add all the numbers together, and all the variables

-6x^2+4x+16=0

a = -6; b = 4; c = +16;
Δ = b2-4ac
Δ = 42-4·(-6)·16
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-20}{2*-6}=\frac{-24}{-12}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+20}{2*-6}=\frac{16}{-12}
=-1+1/3
$