3/4x+8x+16=0

Solution for 3/4x+8x+16=0 equation:

3/4x+8x+16=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

8x+3/4x+16=0

We multiply all the terms by the denominator


8x*4x+16*4x+3=0

Wy multiply elements

32x^2+64x+3=0

a = 32; b = 64; c = +3;
Δ = b2-4ac
Δ = 642-4·32·3
Δ = 3712
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:

$\sqrt{\Delta}=\sqrt{3712}=\sqrt{64*58}=\sqrt{64}*\sqrt{58}=8\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-8\sqrt{58}}{2*32}=\frac{-64-8\sqrt{58}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+8\sqrt{58}}{2*32}=\frac{-64+8\sqrt{58}}{64}
$