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x^2+21x-73.5=0
a = 1; b = 21; c = -73.5;
Δ = b2-4ac
Δ = 212-4·1·(-73.5)
Δ = 735
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{735}=\sqrt{49*15}=\sqrt{49}*\sqrt{15}=7\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-7\sqrt{15}}{2*1}=\frac{-21-7\sqrt{15}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+7\sqrt{15}}{2*1}=\frac{-21+7\sqrt{15}}{2} $
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