0.25x+1/8x+24=60

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

0.25x+1/8x+24=60

We move all terms to the left:

0.25x+1/8x+24-(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

0.25x+1/8x-36=0

We multiply all the terms by the denominator


(0.25x)*8x-36*8x+1=0

We add all the numbers together, and all the variables

(+0.25x)*8x-36*8x+1=0

We multiply parentheses

0x^2-36*8x+1=0

Wy multiply elements

0x^2-288x+1=0

We add all the numbers together, and all the variables

x^2-288x+1=0

a = 1; b = -288; c = +1;
Δ = b2-4ac
Δ = -2882-4·1·1
Δ = 82940
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:

$\sqrt{\Delta}=\sqrt{82940}=\sqrt{4*20735}=\sqrt{4}*\sqrt{20735}=2\sqrt{20735}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-2\sqrt{20735}}{2*1}=\frac{288-2\sqrt{20735}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+2\sqrt{20735}}{2*1}=\frac{288+2\sqrt{20735}}{2}
$