1/2x+x+(x-15)=180

Solution for 1/2x+x+(x-15)=180 equation:

1/2x+x+(x-15)=180

We move all terms to the left:

1/2x+x+(x-15)-(180)=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+1/2x+(x-15)-180=0

We get rid of parentheses

x+1/2x+x-15-180=0

We multiply all the terms by the denominator


x*2x+x*2x-15*2x-180*2x+1=0

Wy multiply elements

2x^2+2x^2-30x-360x+1=0

We add all the numbers together, and all the variables

4x^2-390x+1=0

a = 4; b = -390; c = +1;
Δ = b2-4ac
Δ = -3902-4·4·1
Δ = 152084
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:

$\sqrt{\Delta}=\sqrt{152084}=\sqrt{4*38021}=\sqrt{4}*\sqrt{38021}=2\sqrt{38021}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-390)-2\sqrt{38021}}{2*4}=\frac{390-2\sqrt{38021}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-390)+2\sqrt{38021}}{2*4}=\frac{390+2\sqrt{38021}}{8}
$