x=4x^2+16x+9

Solution for x=4x^2+16x+9 equation:

x=4x^2+16x+9

We move all terms to the left:

x-(4x^2+16x+9)=0

We get rid of parentheses

-4x^2+x-16x-9=0

We add all the numbers together, and all the variables

-4x^2-15x-9=0

a = -4; b = -15; c = -9;
Δ = b2-4ac
Δ = -152-4·(-4)·(-9)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9}{2*-4}=\frac{6}{-8}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9}{2*-4}=\frac{24}{-8}
=-3
$