5/4x-x+2/2=x-1

Solution for 5/4x-x+2/2=x-1 equation:

5/4x-x+2/2=x-1

We move all terms to the left:

5/4x-x+2/2-(x-1)=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+5/4x-(x-1)+1=0

We get rid of parentheses

-1x+5/4x-x+1+1=0

We multiply all the terms by the denominator


-1x*4x-x*4x+1*4x+1*4x+5=0

Wy multiply elements

-4x^2-4x^2+4x+4x+5=0

We add all the numbers together, and all the variables

-8x^2+8x+5=0

a = -8; b = 8; c = +5;
Δ = b2-4ac
Δ = 82-4·(-8)·5
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{14}}{2*-8}=\frac{-8-4\sqrt{14}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{14}}{2*-8}=\frac{-8+4\sqrt{14}}{-16}
$