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X(X-24)=1200
We move all terms to the left:
X(X-24)-(1200)=0
We multiply parentheses
X^2-24X-1200=0
a = 1; b = -24; c = -1200;
Δ = b2-4ac
Δ = -242-4·1·(-1200)
Δ = 5376
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5376}=\sqrt{256*21}=\sqrt{256}*\sqrt{21}=16\sqrt{21}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16\sqrt{21}}{2*1}=\frac{24-16\sqrt{21}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16\sqrt{21}}{2*1}=\frac{24+16\sqrt{21}}{2} $
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