-10x^2+41x-21=0

Solution for -10x^2+41x-21=0 equation:

-10x^2+41x-21=0

a = -10; b = 41; c = -21;
Δ = b2-4ac
Δ = 412-4·(-10)·(-21)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-29}{2*-10}=\frac{-70}{-20}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+29}{2*-10}=\frac{-12}{-20}
=3/5
$