0.25x+1/8x+24x=60

Solution for 0.25x+1/8x+24x=60 equation:

0.25x+1/8x+24x=60

We move all terms to the left:

0.25x+1/8x+24x-(60)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

24.25x+1/8x-60=0

We multiply all the terms by the denominator


(24.25x)*8x-60*8x+1=0

We add all the numbers together, and all the variables

(+24.25x)*8x-60*8x+1=0

We multiply parentheses

192x^2-60*8x+1=0

Wy multiply elements

192x^2-480x+1=0

a = 192; b = -480; c = +1;
Δ = b2-4ac
Δ = -4802-4·192·1
Δ = 229632
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:

$\sqrt{\Delta}=\sqrt{229632}=\sqrt{256*897}=\sqrt{256}*\sqrt{897}=16\sqrt{897}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-16\sqrt{897}}{2*192}=\frac{480-16\sqrt{897}}{384}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+16\sqrt{897}}{2*192}=\frac{480+16\sqrt{897}}{384}
$