x-30+2x-225+1/2x+15=180

Solution for x-30+2x-225+1/2x+15=180 equation:

x-30+2x-225+1/2x+15=180

We move all terms to the left:

x-30+2x-225+1/2x+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

3x+1/2x-420=0

We multiply all the terms by the denominator


3x*2x-420*2x+1=0

Wy multiply elements

6x^2-840x+1=0

a = 6; b = -840; c = +1;
Δ = b2-4ac
Δ = -8402-4·6·1
Δ = 705576
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:

$\sqrt{\Delta}=\sqrt{705576}=\sqrt{4*176394}=\sqrt{4}*\sqrt{176394}=2\sqrt{176394}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-840)-2\sqrt{176394}}{2*6}=\frac{840-2\sqrt{176394}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-840)+2\sqrt{176394}}{2*6}=\frac{840+2\sqrt{176394}}{12}
$