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

Solution for 2/5x+3x-(34)=0 equation:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/5x-34=0

We multiply all the terms by the denominator


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

Wy multiply elements

15x^2-170x+2=0

a = 15; b = -170; c = +2;
Δ = b2-4ac
Δ = -1702-4·15·2
Δ = 28780
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:

$\sqrt{\Delta}=\sqrt{28780}=\sqrt{4*7195}=\sqrt{4}*\sqrt{7195}=2\sqrt{7195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-170)-2\sqrt{7195}}{2*15}=\frac{170-2\sqrt{7195}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-170)+2\sqrt{7195}}{2*15}=\frac{170+2\sqrt{7195}}{30}
$