(x*x)-9x+22=8

Solution for (x*x)-9x+22=8 equation:

(x*x)-9x+22=8

We move all terms to the left:

(x*x)-9x+22-(8)=0

We add all the numbers together, and all the variables

(+x*x)-9x+22-8=0

We add all the numbers together, and all the variables

-9x+(+x*x)+14=0

We get rid of parentheses

-9x+x*x+14=0

Wy multiply elements

x^2-9x+14=0

a = 1; b = -9; c = +14;
Δ = b2-4ac
Δ = -92-4·1·14
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-5}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+5}{2*1}=\frac{14}{2}
=7
$