3x+1/2x=49

Solution for 3x+1/2x=49 equation:

3x+1/2x=49

We move all terms to the left:

3x+1/2x-(49)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


3x*2x-49*2x+1=0

Wy multiply elements

6x^2-98x+1=0

a = 6; b = -98; c = +1;
Δ = b2-4ac
Δ = -982-4·6·1
Δ = 9580
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:

$\sqrt{\Delta}=\sqrt{9580}=\sqrt{4*2395}=\sqrt{4}*\sqrt{2395}=2\sqrt{2395}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-2\sqrt{2395}}{2*6}=\frac{98-2\sqrt{2395}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+2\sqrt{2395}}{2*6}=\frac{98+2\sqrt{2395}}{12}
$