5x+6-1/3x=26

Solution for 5x+6-1/3x=26 equation:

5x+6-1/3x=26

We move all terms to the left:

5x+6-1/3x-(26)=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-1/3x-20=0

We multiply all the terms by the denominator


5x*3x-20*3x-1=0

Wy multiply elements

15x^2-60x-1=0

a = 15; b = -60; c = -1;
Δ = b2-4ac
Δ = -602-4·15·(-1)
Δ = 3660
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:

$\sqrt{\Delta}=\sqrt{3660}=\sqrt{4*915}=\sqrt{4}*\sqrt{915}=2\sqrt{915}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{915}}{2*15}=\frac{60-2\sqrt{915}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{915}}{2*15}=\frac{60+2\sqrt{915}}{30}
$