-21x^2+1800x-3200=0

Solution for -21x^2+1800x-3200=0 equation:

-21x^2+1800x-3200=0

a = -21; b = 1800; c = -3200;
Δ = b2-4ac
Δ = 18002-4·(-21)·(-3200)
Δ = 2971200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2971200}=\sqrt{1600*1857}=\sqrt{1600}*\sqrt{1857}=40\sqrt{1857}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1800)-40\sqrt{1857}}{2*-21}=\frac{-1800-40\sqrt{1857}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1800)+40\sqrt{1857}}{2*-21}=\frac{-1800+40\sqrt{1857}}{-42}
$