3a^2-9a-79=11-a^2

Solution for 3a^2-9a-79=11-a^2 equation:

3a^2-9a-79=11-a^2

We move all terms to the left:

3a^2-9a-79-(11-a^2)=0

We get rid of parentheses

3a^2+a^2-9a-11-79=0

We add all the numbers together, and all the variables

4a^2-9a-90=0

a = 4; b = -9; c = -90;
Δ = b2-4ac
Δ = -92-4·4·(-90)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-39}{2*4}=\frac{-30}{8}
=-3+3/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+39}{2*4}=\frac{48}{8}
=6
$