3x+1/2x+x=110

Solution for 3x+1/2x+x=110 equation:

3x+1/2x+x=110

We move all terms to the left:

3x+1/2x+x-(110)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/2x-110=0

We multiply all the terms by the denominator


4x*2x-110*2x+1=0

Wy multiply elements

8x^2-220x+1=0

a = 8; b = -220; c = +1;
Δ = b2-4ac
Δ = -2202-4·8·1
Δ = 48368
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:

$\sqrt{\Delta}=\sqrt{48368}=\sqrt{16*3023}=\sqrt{16}*\sqrt{3023}=4\sqrt{3023}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-220)-4\sqrt{3023}}{2*8}=\frac{220-4\sqrt{3023}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-220)+4\sqrt{3023}}{2*8}=\frac{220+4\sqrt{3023}}{16}
$