-1/2x-(x-9)=10x

Solution for -1/2x-(x-9)=10x equation:

-1/2x-(x-9)=10x

We move all terms to the left:

-1/2x-(x-9)-(10x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-10x-1/2x-(x-9)=0

We get rid of parentheses

-10x-1/2x-x+9=0

We multiply all the terms by the denominator


-10x*2x-x*2x+9*2x-1=0

Wy multiply elements

-20x^2-2x^2+18x-1=0

We add all the numbers together, and all the variables

-22x^2+18x-1=0

a = -22; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·(-22)·(-1)
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{59}}{2*-22}=\frac{-18-2\sqrt{59}}{-44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{59}}{2*-22}=\frac{-18+2\sqrt{59}}{-44}
$