10a^2+9a=9

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

10a^2+9a=9

We move all terms to the left:

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

a = 10; b = 9; c = -9;
Δ = b2-4ac
Δ = 92-4·10·(-9)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-21}{2*10}=\frac{-30}{20}
=-1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+21}{2*10}=\frac{12}{20}
=3/5
$