3+.25x=1/8x-2

Solution for 3+.25x=1/8x-2 equation:

3+.25x=1/8x-2

We move all terms to the left:

3+.25x-(1/8x-2)=0


Domain of the equation: 8x-2)!=0

x∈R


We get rid of parentheses

.25x-1/8x+2+3=0

We multiply all the terms by the denominator


(.25x)*8x+2*8x+3*8x-1=0

We add all the numbers together, and all the variables

(+.25x)*8x+2*8x+3*8x-1=0

We multiply parentheses

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

Wy multiply elements

8x^2+16x+24x-1=0

We add all the numbers together, and all the variables

8x^2+40x-1=0

a = 8; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·8·(-1)
Δ = 1632
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:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{102}}{2*8}=\frac{-40-4\sqrt{102}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{102}}{2*8}=\frac{-40+4\sqrt{102}}{16}
$