3/4x+2/3x=34

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

3/4x+2/3x=34

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


9x/12x^2+8x/12x^2-34=0

We multiply all the terms by the denominator


9x+8x-34*12x^2=0

We add all the numbers together, and all the variables

17x-34*12x^2=0

Wy multiply elements

-408x^2+17x=0

a = -408; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-408)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-408}=\frac{-34}{-816}
=1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-408}=\frac{0}{-816}
=0
$