6r2-r-77=0

Solution for 6r2-r-77=0 equation:

6r^2-r-77=0

We add all the numbers together, and all the variables

6r^2-1r-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:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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