5-x+2/4X-3=x-1

Solution for 5-x+2/4X-3=x-1 equation:

5-x+2/4x-3=x-1

We move all terms to the left:

5-x+2/4x-3-(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+2/4x-(x-1)+2=0

We get rid of parentheses

-1x+2/4x-x+1+2=0

We multiply all the terms by the denominator


-1x*4x-x*4x+1*4x+2*4x+2=0

Wy multiply elements

-4x^2-4x^2+4x+8x+2=0

We add all the numbers together, and all the variables

-8x^2+12x+2=0

a = -8; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·(-8)·2
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{13}}{2*-8}=\frac{-12-4\sqrt{13}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{13}}{2*-8}=\frac{-12+4\sqrt{13}}{-16}
$