3/4x-5+x-1-1=22

Solution for 3/4x-5+x-1-1=22 equation:

3/4x-5+x-1-1=22

We move all terms to the left:

3/4x-5+x-1-1-(22)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/4x-29=0

We multiply all the terms by the denominator


x*4x-29*4x+3=0

Wy multiply elements

4x^2-116x+3=0

a = 4; b = -116; c = +3;
Δ = b2-4ac
Δ = -1162-4·4·3
Δ = 13408
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:

$\sqrt{\Delta}=\sqrt{13408}=\sqrt{16*838}=\sqrt{16}*\sqrt{838}=4\sqrt{838}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-4\sqrt{838}}{2*4}=\frac{116-4\sqrt{838}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+4\sqrt{838}}{2*4}=\frac{116+4\sqrt{838}}{8}
$