X+3/4x+x=22

Solution for X+3/4x+x=22 equation:

X+3/4X+X=22

We move all terms to the left:

X+3/4X+X-(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

2X+3/4X-22=0

We multiply all the terms by the denominator


2X*4X-22*4X+3=0

Wy multiply elements

8X^2-88X+3=0

a = 8; b = -88; c = +3;
Δ = b2-4ac
Δ = -882-4·8·3
Δ = 7648
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:

$\sqrt{\Delta}=\sqrt{7648}=\sqrt{16*478}=\sqrt{16}*\sqrt{478}=4\sqrt{478}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-4\sqrt{478}}{2*8}=\frac{88-4\sqrt{478}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+4\sqrt{478}}{2*8}=\frac{88+4\sqrt{478}}{16}
$