3-0.25x=1/2x+9

Solution for 3-0.25x=1/2x+9 equation:

3-0.25x=1/2x+9

We move all terms to the left:

3-0.25x-(1/2x+9)=0


Domain of the equation: 2x+9)!=0

x∈R


We get rid of parentheses

-0.25x-1/2x-9+3=0

We multiply all the terms by the denominator


-(0.25x)*2x-9*2x+3*2x-1=0

We add all the numbers together, and all the variables

-(+0.25x)*2x-9*2x+3*2x-1=0

We multiply parentheses

-0x^2-9*2x+3*2x-1=0

Wy multiply elements

-0x^2-18x+6x-1=0

We add all the numbers together, and all the variables

-1x^2-12x-1=0

a = -1; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·(-1)·(-1)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{35}}{2*-1}=\frac{12-2\sqrt{35}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{35}}{2*-1}=\frac{12+2\sqrt{35}}{-2}
$