-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

-1x-1/4x+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 = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{77}}{2*-4}=\frac{-18-2\sqrt{77}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{77}}{2*-4}=\frac{-18+2\sqrt{77}}{-8}
$