3x+21/2x=65

Solution for 3x+21/2x=65 equation:

3x+21/2x=65

We move all terms to the left:

3x+21/2x-(65)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


3x*2x-65*2x+21=0

Wy multiply elements

6x^2-130x+21=0

a = 6; b = -130; c = +21;
Δ = b2-4ac
Δ = -1302-4·6·21
Δ = 16396
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:

$\sqrt{\Delta}=\sqrt{16396}=\sqrt{4*4099}=\sqrt{4}*\sqrt{4099}=2\sqrt{4099}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{4099}}{2*6}=\frac{130-2\sqrt{4099}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{4099}}{2*6}=\frac{130+2\sqrt{4099}}{12}
$