14/3x+2x-5=15

Solution for 14/3x+2x-5=15 equation:

14/3x+2x-5=15

We move all terms to the left:

14/3x+2x-5-(15)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x+14/3x-20=0

We multiply all the terms by the denominator


2x*3x-20*3x+14=0

Wy multiply elements

6x^2-60x+14=0

a = 6; b = -60; c = +14;
Δ = b2-4ac
Δ = -602-4·6·14
Δ = 3264
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:

$\sqrt{\Delta}=\sqrt{3264}=\sqrt{64*51}=\sqrt{64}*\sqrt{51}=8\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-8\sqrt{51}}{2*6}=\frac{60-8\sqrt{51}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+8\sqrt{51}}{2*6}=\frac{60+8\sqrt{51}}{12}
$