2/3x+5x=34

Solution for 2/3x+5x=34 equation:

2/3x+5x=34

We move all terms to the left:

2/3x+5x-(34)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5x+2/3x-34=0

We multiply all the terms by the denominator


5x*3x-34*3x+2=0

Wy multiply elements

15x^2-102x+2=0

a = 15; b = -102; c = +2;
Δ = b2-4ac
Δ = -1022-4·15·2
Δ = 10284
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:

$\sqrt{\Delta}=\sqrt{10284}=\sqrt{4*2571}=\sqrt{4}*\sqrt{2571}=2\sqrt{2571}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-2\sqrt{2571}}{2*15}=\frac{102-2\sqrt{2571}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+2\sqrt{2571}}{2*15}=\frac{102+2\sqrt{2571}}{30}
$