8r^2-46r-112=0

Solution for 8r^2-46r-112=0 equation:

8r^2-46r-112=0

a = 8; b = -46; c = -112;
Δ = b2-4ac
Δ = -462-4·8·(-112)
Δ = 5700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5700}=\sqrt{100*57}=\sqrt{100}*\sqrt{57}=10\sqrt{57}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-10\sqrt{57}}{2*8}=\frac{46-10\sqrt{57}}{16}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+10\sqrt{57}}{2*8}=\frac{46+10\sqrt{57}}{16}
$