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5X^2-102X-216=0
a = 5; b = -102; c = -216;
Δ = b2-4ac
Δ = -1022-4·5·(-216)
Δ = 14724
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14724}=\sqrt{36*409}=\sqrt{36}*\sqrt{409}=6\sqrt{409}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-6\sqrt{409}}{2*5}=\frac{102-6\sqrt{409}}{10} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+6\sqrt{409}}{2*5}=\frac{102+6\sqrt{409}}{10} $
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