3/2x+4x=22

Solution for 3/2x+4x=22 equation:

3/2x+4x=22

We move all terms to the left:

3/2x+4x-(22)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4x+3/2x-22=0

We multiply all the terms by the denominator


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

Wy multiply elements

8x^2-44x+3=0

a = 8; b = -44; c = +3;
Δ = b2-4ac
Δ = -442-4·8·3
Δ = 1840
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:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{115}}{2*8}=\frac{44-4\sqrt{115}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{115}}{2*8}=\frac{44+4\sqrt{115}}{16}
$