x+4/4x+16=0

Solution for x+4/4x+16=0 equation:

x+4/4x+16=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x+16*4x+4=0

Wy multiply elements

4x^2+64x+4=0

a = 4; b = 64; c = +4;
Δ = b2-4ac
Δ = 642-4·4·4
Δ = 4032
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:

$\sqrt{\Delta}=\sqrt{4032}=\sqrt{576*7}=\sqrt{576}*\sqrt{7}=24\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-24\sqrt{7}}{2*4}=\frac{-64-24\sqrt{7}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+24\sqrt{7}}{2*4}=\frac{-64+24\sqrt{7}}{8}
$