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X^2+6X-3780=0
a = 1; b = 6; c = -3780;
Δ = b2-4ac
Δ = 62-4·1·(-3780)
Δ = 15156
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{15156}=\sqrt{36*421}=\sqrt{36}*\sqrt{421}=6\sqrt{421}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{421}}{2*1}=\frac{-6-6\sqrt{421}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{421}}{2*1}=\frac{-6+6\sqrt{421}}{2} $
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