(x*x)-9+(x-3)(-2x+7)=0

Solution for (x*x)-9+(x-3)(-2x+7)=0 equation:

(x*x)-9+(x-3)(-2x+7)=0

We add all the numbers together, and all the variables

(+x*x)+(x-3)(-2x+7)-9=0

We get rid of parentheses

x*x+(x-3)(-2x+7)-9=0

We multiply parentheses ..

(-2x^2+7x+6x-21)+x*x-9=0

Wy multiply elements

(-2x^2+7x+6x-21)+x^2-9=0

We get rid of parentheses

-2x^2+x^2+7x+6x-21-9=0

We add all the numbers together, and all the variables

-1x^2+13x-30=0

a = -1; b = 13; c = -30;
Δ = b2-4ac
Δ = 132-4·(-1)·(-30)
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{-(13)-7}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+7}{2*-1}=\frac{-6}{-2}
=+3
$