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-1.2x^2+97.2x-1464=216
We move all terms to the left:
-1.2x^2+97.2x-1464-(216)=0
We add all the numbers together, and all the variables
-1.2x^2+97.2x-1680=0
a = -1.2; b = 97.2; c = -1680;
Δ = b2-4ac
Δ = 97.22-4·(-1.2)·(-1680)
Δ = 1383.84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(97.2)-\sqrt{1383.84}}{2*-1.2}=\frac{-97.2-\sqrt{1383.84}}{-2.4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(97.2)+\sqrt{1383.84}}{2*-1.2}=\frac{-97.2+\sqrt{1383.84}}{-2.4} $
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