9-3/4x=x-5

Solution for 9-3/4x=x-5 equation:

9-3/4x=x-5

We move all terms to the left:

9-3/4x-(x-5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

-3/4x-x+5+9=0

We multiply all the terms by the denominator


-x*4x+5*4x+9*4x-3=0

Wy multiply elements

-4x^2+20x+36x-3=0

We add all the numbers together, and all the variables

-4x^2+56x-3=0

a = -4; b = 56; c = -3;
Δ = b2-4ac
Δ = 562-4·(-4)·(-3)
Δ = 3088
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:

$\sqrt{\Delta}=\sqrt{3088}=\sqrt{16*193}=\sqrt{16}*\sqrt{193}=4\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{193}}{2*-4}=\frac{-56-4\sqrt{193}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{193}}{2*-4}=\frac{-56+4\sqrt{193}}{-8}
$