1/4x+9=-16x

Solution for 1/4x+9=-16x equation:

1/4x+9=-16x

We move all terms to the left:

1/4x+9-(-16x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x+16x+9=0

We multiply all the terms by the denominator


16x*4x+9*4x+1=0

Wy multiply elements

64x^2+36x+1=0

a = 64; b = 36; c = +1;
Δ = b2-4ac
Δ = 362-4·64·1
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{65}}{2*64}=\frac{-36-4\sqrt{65}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{65}}{2*64}=\frac{-36+4\sqrt{65}}{128}
$