-21r^2-r+10=0

Solution for -21r^2-r+10=0 equation:

-21r^2-r+10=0

We add all the numbers together, and all the variables

-21r^2-1r+10=0

a = -21; b = -1; c = +10;
Δ = b2-4ac
Δ = -12-4·(-21)·10
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-29}{2*-21}=\frac{-28}{-42}
=2/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+29}{2*-21}=\frac{30}{-42}
=-5/7
$