3/2x+X=120

Solution for 3/2x+X=120 equation:

3/2x+x=120

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/2x-120=0

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2-240x+3=0

a = 2; b = -240; c = +3;
Δ = b2-4ac
Δ = -2402-4·2·3
Δ = 57576
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:

$\sqrt{\Delta}=\sqrt{57576}=\sqrt{4*14394}=\sqrt{4}*\sqrt{14394}=2\sqrt{14394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-2\sqrt{14394}}{2*2}=\frac{240-2\sqrt{14394}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+2\sqrt{14394}}{2*2}=\frac{240+2\sqrt{14394}}{4}
$