2x+21/3x=75

Solution for 2x+21/3x=75 equation:

2x+21/3x=75

We move all terms to the left:

2x+21/3x-(75)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


2x*3x-75*3x+21=0

Wy multiply elements

6x^2-225x+21=0

a = 6; b = -225; c = +21;
Δ = b2-4ac
Δ = -2252-4·6·21
Δ = 50121
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:

$\sqrt{\Delta}=\sqrt{50121}=\sqrt{9*5569}=\sqrt{9}*\sqrt{5569}=3\sqrt{5569}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-225)-3\sqrt{5569}}{2*6}=\frac{225-3\sqrt{5569}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-225)+3\sqrt{5569}}{2*6}=\frac{225+3\sqrt{5569}}{12}
$