3/2x+11/4x=34

Solution for 3/2x+11/4x=34 equation:

3/2x+11/4x=34

We move all terms to the left:

3/2x+11/4x-(34)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


12x/8x^2+22x/8x^2-34=0

We multiply all the terms by the denominator


12x+22x-34*8x^2=0

We add all the numbers together, and all the variables

34x-34*8x^2=0

Wy multiply elements

-272x^2+34x=0

a = -272; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·(-272)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*-272}=\frac{-68}{-544}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*-272}=\frac{0}{-544}
=0
$