x*x-3x-5=2x+9

Solution for x*x-3x-5=2x+9 equation:

x*x-3x-5=2x+9

We move all terms to the left:

x*x-3x-5-(2x+9)=0

We add all the numbers together, and all the variables

-3x+x*x-(2x+9)-5=0

Wy multiply elements

x^2-3x-(2x+9)-5=0

We get rid of parentheses

x^2-3x-2x-9-5=0

We add all the numbers together, and all the variables

x^2-5x-14=0

a = 1; b = -5; c = -14;
Δ = b2-4ac
Δ = -52-4·1·(-14)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-9}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+9}{2*1}=\frac{14}{2}
=7
$