9-51/2x-3(-2x+1)=x

Solution for 9-51/2x-3(-2x+1)=x equation:

9-51/2x-3(-2x+1)=x

We move all terms to the left:

9-51/2x-3(-2x+1)-(x)=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-51/2x-3(-2x+1)+9=0

We multiply parentheses

-1x-51/2x+6x-3+9=0

We multiply all the terms by the denominator


-1x*2x+6x*2x-3*2x+9*2x-51=0

Wy multiply elements

-2x^2+12x^2-6x+18x-51=0

We add all the numbers together, and all the variables

10x^2+12x-51=0

a = 10; b = 12; c = -51;
Δ = b2-4ac
Δ = 122-4·10·(-51)
Δ = 2184
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:

$\sqrt{\Delta}=\sqrt{2184}=\sqrt{4*546}=\sqrt{4}*\sqrt{546}=2\sqrt{546}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{546}}{2*10}=\frac{-12-2\sqrt{546}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{546}}{2*10}=\frac{-12+2\sqrt{546}}{20}
$