10a^2-20a-77=3

Solution for 10a^2-20a-77=3 equation:

10a^2-20a-77=3

We move all terms to the left:

10a^2-20a-77-(3)=0

We add all the numbers together, and all the variables

10a^2-20a-80=0

a = 10; b = -20; c = -80;
Δ = b2-4ac
Δ = -202-4·10·(-80)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-60}{2*10}=\frac{-40}{20}
=-2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+60}{2*10}=\frac{80}{20}
=4
$