3/4x+3/2x=1+22

Solution for 3/4x+3/2x=1+22 equation:

3/4x+3/2x=1+22

We move all terms to the left:

3/4x+3/2x-(1+22)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x+3/2x-23=0

We calculate fractions


6x/8x^2+12x/8x^2-23=0

We multiply all the terms by the denominator


6x+12x-23*8x^2=0

We add all the numbers together, and all the variables

18x-23*8x^2=0

Wy multiply elements

-184x^2+18x=0

a = -184; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-184)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-184}=\frac{-36}{-368}
=9/92
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-184}=\frac{0}{-368}
=0
$