a^2-10a=-9

Solution for a^2-10a=-9 equation:

a^2-10a=-9

We move all terms to the left:

a^2-10a-(-9)=0

We add all the numbers together, and all the variables

a^2-10a+9=0

a = 1; b = -10; c = +9;
Δ = b2-4ac
Δ = -102-4·1·9
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8}{2*1}=\frac{2}{2}
=1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8}{2*1}=\frac{18}{2}
=9
$