1/4x=x-24

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

1/4x=x-24

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-x+24=0

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2+96x+1=0

a = -4; b = 96; c = +1;
Δ = b2-4ac
Δ = 962-4·(-4)·1
Δ = 9232
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:

$\sqrt{\Delta}=\sqrt{9232}=\sqrt{16*577}=\sqrt{16}*\sqrt{577}=4\sqrt{577}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-4\sqrt{577}}{2*-4}=\frac{-96-4\sqrt{577}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+4\sqrt{577}}{2*-4}=\frac{-96+4\sqrt{577}}{-8}
$