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X2+6X-374=0
We add all the numbers together, and all the variables
X^2+6X-374=0
a = 1; b = 6; c = -374;
Δ = b2-4ac
Δ = 62-4·1·(-374)
Δ = 1532
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1532}=\sqrt{4*383}=\sqrt{4}*\sqrt{383}=2\sqrt{383}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{383}}{2*1}=\frac{-6-2\sqrt{383}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{383}}{2*1}=\frac{-6+2\sqrt{383}}{2} $
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