3x+1/2x=350

Solution for 3x+1/2x=350 equation:

3x+1/2x=350

We move all terms to the left:

3x+1/2x-(350)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


3x*2x-350*2x+1=0

Wy multiply elements

6x^2-700x+1=0

a = 6; b = -700; c = +1;
Δ = b2-4ac
Δ = -7002-4·6·1
Δ = 489976
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:

$\sqrt{\Delta}=\sqrt{489976}=\sqrt{4*122494}=\sqrt{4}*\sqrt{122494}=2\sqrt{122494}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-700)-2\sqrt{122494}}{2*6}=\frac{700-2\sqrt{122494}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-700)+2\sqrt{122494}}{2*6}=\frac{700+2\sqrt{122494}}{12}
$