2(x^2-9)+5x=2x-x^2

Solution for 2(x^2-9)+5x=2x-x^2 equation:

2(x^2-9)+5x=2x-x^2

We move all terms to the left:

2(x^2-9)+5x-(2x-x^2)=0

We add all the numbers together, and all the variables

-(2x-x^2)+5x+2(x^2-9)=0

We multiply parentheses

-(2x-x^2)+2x^2+5x-18=0

We get rid of parentheses

x^2+2x^2-2x+5x-18=0

We add all the numbers together, and all the variables

3x^2+3x-18=0

a = 3; b = 3; c = -18;
Δ = b2-4ac
Δ = 32-4·3·(-18)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-15}{2*3}=\frac{-18}{6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+15}{2*3}=\frac{12}{6}
=2
$