-21x^2-11x+2=0

Solution for -21x^2-11x+2=0 equation:

-21x^2-11x+2=0

a = -21; b = -11; c = +2;
Δ = b2-4ac
Δ = -112-4·(-21)·2
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-17}{2*-21}=\frac{-6}{-42}
=1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+17}{2*-21}=\frac{28}{-42}
=-2/3
$