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X^2+111X+24=0
a = 1; b = 111; c = +24;
Δ = b2-4ac
Δ = 1112-4·1·24
Δ = 12225
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12225}=\sqrt{25*489}=\sqrt{25}*\sqrt{489}=5\sqrt{489}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(111)-5\sqrt{489}}{2*1}=\frac{-111-5\sqrt{489}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(111)+5\sqrt{489}}{2*1}=\frac{-111+5\sqrt{489}}{2} $
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