1/2*3x+x=120

Solution for 1/2*3x+x=120 equation:

1/2*3x+x=120

We move all terms to the left:

1/2*3x+x-(120)=0


Domain of the equation: 2*3x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/2*3x-120=0

We multiply all the terms by the denominator


x*2*3x-120*2*3x+1=0

Wy multiply elements

6x^2*3-720x*3+1=0

Wy multiply elements

18x^2-2160x+1=0

a = 18; b = -2160; c = +1;
Δ = b2-4ac
Δ = -21602-4·18·1
Δ = 4665528
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:

$\sqrt{\Delta}=\sqrt{4665528}=\sqrt{36*129598}=\sqrt{36}*\sqrt{129598}=6\sqrt{129598}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2160)-6\sqrt{129598}}{2*18}=\frac{2160-6\sqrt{129598}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2160)+6\sqrt{129598}}{2*18}=\frac{2160+6\sqrt{129598}}{36}
$