1/2x+15=x-30+2x-120

Solution for 1/2x+15=x-30+2x-120 equation:

1/2x+15=x-30+2x-120

We move all terms to the left:

1/2x+15-(x-30+2x-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

1/2x-(3x-150)+15=0

We get rid of parentheses

1/2x-3x+150+15=0

We multiply all the terms by the denominator


-3x*2x+150*2x+15*2x+1=0

Wy multiply elements

-6x^2+300x+30x+1=0

We add all the numbers together, and all the variables

-6x^2+330x+1=0

a = -6; b = 330; c = +1;
Δ = b2-4ac
Δ = 3302-4·(-6)·1
Δ = 108924
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:

$\sqrt{\Delta}=\sqrt{108924}=\sqrt{4*27231}=\sqrt{4}*\sqrt{27231}=2\sqrt{27231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(330)-2\sqrt{27231}}{2*-6}=\frac{-330-2\sqrt{27231}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(330)+2\sqrt{27231}}{2*-6}=\frac{-330+2\sqrt{27231}}{-12}
$