1/4x=4x+24

Solution for 1/4x=4x+24 equation:

1/4x=4x+24

We move all terms to the left:

1/4x-(4x+24)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-4x-24=0

We multiply all the terms by the denominator


-4x*4x-24*4x+1=0

Wy multiply elements

-16x^2-96x+1=0

a = -16; b = -96; c = +1;
Δ = b2-4ac
Δ = -962-4·(-16)·1
Δ = 9280
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:

$\sqrt{\Delta}=\sqrt{9280}=\sqrt{64*145}=\sqrt{64}*\sqrt{145}=8\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-8\sqrt{145}}{2*-16}=\frac{96-8\sqrt{145}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+8\sqrt{145}}{2*-16}=\frac{96+8\sqrt{145}}{-32}
$