5/4x+21-x=48

Solution for 5/4x+21-x=48 equation:

5/4x+21-x=48

We move all terms to the left:

5/4x+21-x-(48)=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-27=0

We multiply all the terms by the denominator


-1x*4x-27*4x+5=0

Wy multiply elements

-4x^2-108x+5=0

a = -4; b = -108; c = +5;
Δ = b2-4ac
Δ = -1082-4·(-4)·5
Δ = 11744
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:

$\sqrt{\Delta}=\sqrt{11744}=\sqrt{16*734}=\sqrt{16}*\sqrt{734}=4\sqrt{734}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-4\sqrt{734}}{2*-4}=\frac{108-4\sqrt{734}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+4\sqrt{734}}{2*-4}=\frac{108+4\sqrt{734}}{-8}
$