10a^2-20a-39=-9

Solution for 10a^2-20a-39=-9 equation:

10a^2-20a-39=-9

We move all terms to the left:

10a^2-20a-39-(-9)=0

We add all the numbers together, and all the variables

10a^2-20a-30=0

a = 10; b = -20; c = -30;
Δ = b2-4ac
Δ = -202-4·10·(-30)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-40}{2*10}=\frac{-20}{20}
=-1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+40}{2*10}=\frac{60}{20}
=3
$