6x-(2x-1)=9x+2(2-x2)

Solution for 6x-(2x-1)=9x+2(2-x2) equation:

6x-(2x-1)=9x+2(2-x2)

We move all terms to the left:

6x-(2x-1)-(9x+2(2-x2))=0

We add all the numbers together, and all the variables

-(9x+2(-1x^2+2))+6x-(2x-1)=0

We get rid of parentheses

-(9x+2(-1x^2+2))+6x-2x+1=0


We calculate terms in parentheses: -(9x+2(-1x^2+2)), so:

9x+2(-1x^2+2)

determiningTheFunctionDomain
2(-1x^2+2)+9x

We multiply parentheses

-2x^2+9x+4

Back to the equation:

-(-2x^2+9x+4)


We add all the numbers together, and all the variables

-(-2x^2+9x+4)+4x+1=0

We get rid of parentheses

2x^2-9x+4x-4+1=0

We add all the numbers together, and all the variables

2x^2-5x-3=0

a = 2; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·2·(-3)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*2}=\frac{-2}{4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*2}=\frac{12}{4}
=3
$