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-14x^2+1680x-49.000=0
We add all the numbers together, and all the variables
-14x^2+1680x-49=0
a = -14; b = 1680; c = -49;
Δ = b2-4ac
Δ = 16802-4·(-14)·(-49)
Δ = 2819656
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2819656}=\sqrt{196*14386}=\sqrt{196}*\sqrt{14386}=14\sqrt{14386}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1680)-14\sqrt{14386}}{2*-14}=\frac{-1680-14\sqrt{14386}}{-28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1680)+14\sqrt{14386}}{2*-14}=\frac{-1680+14\sqrt{14386}}{-28} $
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