77r^2+3r-54=0

Solution for 77r^2+3r-54=0 equation:

77r^2+3r-54=0

a = 77; b = 3; c = -54;
Δ = b2-4ac
Δ = 32-4·77·(-54)
Δ = 16641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16641}=129$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-129}{2*77}=\frac{-132}{154}
=-6/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+129}{2*77}=\frac{126}{154}
=9/11
$