-1/2x-9-30-x=15

Solution for -1/2x-9-30-x=15 equation:

-1/2x-9-30-x=15

We move all terms to the left:

-1/2x-9-30-x-(15)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x-1/2x-54=0

We multiply all the terms by the denominator


-1x*2x-54*2x-1=0

Wy multiply elements

-2x^2-108x-1=0

a = -2; b = -108; c = -1;
Δ = b2-4ac
Δ = -1082-4·(-2)·(-1)
Δ = 11656
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:

$\sqrt{\Delta}=\sqrt{11656}=\sqrt{4*2914}=\sqrt{4}*\sqrt{2914}=2\sqrt{2914}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-2\sqrt{2914}}{2*-2}=\frac{108-2\sqrt{2914}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+2\sqrt{2914}}{2*-2}=\frac{108+2\sqrt{2914}}{-4}
$