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-3x^2+84x+800=0
a = -3; b = 84; c = +800;
Δ = b2-4ac
Δ = 842-4·(-3)·800
Δ = 16656
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16656}=\sqrt{16*1041}=\sqrt{16}*\sqrt{1041}=4\sqrt{1041}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{1041}}{2*-3}=\frac{-84-4\sqrt{1041}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{1041}}{2*-3}=\frac{-84+4\sqrt{1041}}{-6} $
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