10r^2-47r-42=0

Solution for 10r^2-47r-42=0 equation:

10r^2-47r-42=0

a = 10; b = -47; c = -42;
Δ = b2-4ac
Δ = -472-4·10·(-42)
Δ = 3889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-\sqrt{3889}}{2*10}=\frac{47-\sqrt{3889}}{20}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{3889}}{2*10}=\frac{47+\sqrt{3889}}{20}
$