2x(2)-9=-x(2)+2x-2

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

2x(2)-9=-x(2)+2x-2

We move all terms to the left:

2x(2)-9-(-x(2)+2x-2)=0

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-2x-7=0

a = 3; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·3·(-7)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{22}}{2*3}=\frac{2-2\sqrt{22}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{22}}{2*3}=\frac{2+2\sqrt{22}}{6}
$