6a^2=a+77

Solution for 6a^2=a+77 equation:

6a^2=a+77

We move all terms to the left:

6a^2-(a+77)=0

We get rid of parentheses

6a^2-a-77=0

We add all the numbers together, and all the variables

6a^2-1a-77=0

a = 6; b = -1; c = -77;
Δ = b2-4ac
Δ = -12-4·6·(-77)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-43}{2*6}=\frac{-42}{12}
=-3+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+43}{2*6}=\frac{44}{12}
=3+2/3
$