1/2x+3x-176=0

Solution for 1/2x+3x-176=0 equation:

1/2x+3x-176=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/2x-176=0

We multiply all the terms by the denominator


3x*2x-176*2x+1=0

Wy multiply elements

6x^2-352x+1=0

a = 6; b = -352; c = +1;
Δ = b2-4ac
Δ = -3522-4·6·1
Δ = 123880
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:

$\sqrt{\Delta}=\sqrt{123880}=\sqrt{4*30970}=\sqrt{4}*\sqrt{30970}=2\sqrt{30970}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-352)-2\sqrt{30970}}{2*6}=\frac{352-2\sqrt{30970}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-352)+2\sqrt{30970}}{2*6}=\frac{352+2\sqrt{30970}}{12}
$