7r^2-54r-16=0

Solution for 7r^2-54r-16=0 equation:

7r^2-54r-16=0

a = 7; b = -54; c = -16;
Δ = b2-4ac
Δ = -542-4·7·(-16)
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-58}{2*7}=\frac{-4}{14}
=-2/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+58}{2*7}=\frac{112}{14}
=8
$