-1/4x+3.25=x-3

Solution for -1/4x+3.25=x-3 equation:

-1/4x+3.25=x-3

We move all terms to the left:

-1/4x+3.25-(x-3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

-1/4x-x+3+3.25=0

We multiply all the terms by the denominator


-x*4x+3*4x+(3.25)*4x-1=0

We multiply parentheses

-x*4x+3*4x+13x-1=0

Wy multiply elements

-4x^2+12x+13x-1=0

We add all the numbers together, and all the variables

-4x^2+25x-1=0

a = -4; b = 25; c = -1;
Δ = b2-4ac
Δ = 252-4·(-4)·(-1)
Δ = 609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{609}}{2*-4}=\frac{-25-\sqrt{609}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{609}}{2*-4}=\frac{-25+\sqrt{609}}{-8}
$