0.25x=1/3x-8

Solution for 0.25x=1/3x-8 equation:

0.25x=1/3x-8

We move all terms to the left:

0.25x-(1/3x-8)=0


Domain of the equation: 3x-8)!=0

x∈R


We get rid of parentheses

0.25x-1/3x+8=0

We multiply all the terms by the denominator


(0.25x)*3x+8*3x-1=0

We add all the numbers together, and all the variables

(+0.25x)*3x+8*3x-1=0

We multiply parentheses

0x^2+8*3x-1=0

Wy multiply elements

0x^2+24x-1=0

We add all the numbers together, and all the variables

x^2+24x-1=0

a = 1; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·1·(-1)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{145}}{2*1}=\frac{-24-2\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{145}}{2*1}=\frac{-24+2\sqrt{145}}{2}
$