(x-3)(x+3)+2x^2=-5x-7

Solution for (x-3)(x+3)+2x^2=-5x-7 equation:

(x-3)(x+3)+2x^2=-5x-7

We move all terms to the left:

(x-3)(x+3)+2x^2-(-5x-7)=0

We use the square of the difference formula

2x^2+x^2-(-5x-7)-9=0

We get rid of parentheses

2x^2+x^2+5x+7-9=0

We add all the numbers together, and all the variables

3x^2+5x-2=0

a = 3; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·3·(-2)
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*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*3}=\frac{2}{6}
=1/3
$