-1/4x+4.5=-x

Solution for -1/4x+4.5=-x equation:

-1/4x+4.5=-x

We move all terms to the left:

-1/4x+4.5-(-x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1/4x-(-1x)+4.5=0

We get rid of parentheses

-1/4x+1x+4.5=0

We multiply all the terms by the denominator


1x*4x+(4.5)*4x-1=0

We multiply parentheses

1x*4x+18x-1=0

Wy multiply elements

4x^2+18x-1=0

a = 4; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·4·(-1)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{85}}{2*4}=\frac{-18-2\sqrt{85}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{85}}{2*4}=\frac{-18+2\sqrt{85}}{8}
$