-5x2-8x+21=0

Solution for -5x2-8x+21=0 equation:

-5x^2-8x+21=0

a = -5; b = -8; c = +21;
Δ = b2-4ac
Δ = -82-4·(-5)·21
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-22}{2*-5}=\frac{-14}{-10}
=1+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+22}{2*-5}=\frac{30}{-10}
=-3
$