3-0.25x=-1/2x+8

Solution for 3-0.25x=-1/2x+8 equation:

3-0.25x=-1/2x+8

We move all terms to the left:

3-0.25x-(-1/2x+8)=0


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

x∈R


We get rid of parentheses

-0.25x+1/2x-8+3=0

We multiply all the terms by the denominator


-(0.25x)*2x-8*2x+3*2x+1=0

We add all the numbers together, and all the variables

-(+0.25x)*2x-8*2x+3*2x+1=0

We multiply parentheses

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

Wy multiply elements

-0x^2-16x+6x+1=0

We add all the numbers together, and all the variables

-1x^2-10x+1=0

a = -1; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·(-1)·1
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{26}}{2*-1}=\frac{10-2\sqrt{26}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{26}}{2*-1}=\frac{10+2\sqrt{26}}{-2}
$