x+3/4x=22

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

x+3/4x=22

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


x*4x-22*4x+3=0

Wy multiply elements

4x^2-88x+3=0

a = 4; b = -88; c = +3;
Δ = b2-4ac
Δ = -882-4·4·3
Δ = 7696
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:

$\sqrt{\Delta}=\sqrt{7696}=\sqrt{16*481}=\sqrt{16}*\sqrt{481}=4\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-4\sqrt{481}}{2*4}=\frac{88-4\sqrt{481}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+4\sqrt{481}}{2*4}=\frac{88+4\sqrt{481}}{8}
$