-0.25x=-1/2x+9

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

-0.25x=-1/2x+9

We move all terms to the left:

-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=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -1; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·(-1)·1
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{82}}{2*-1}=\frac{18-2\sqrt{82}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{82}}{2*-1}=\frac{18+2\sqrt{82}}{-2}
$