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X^2-117X+810=0
a = 1; b = -117; c = +810;
Δ = b2-4ac
Δ = -1172-4·1·810
Δ = 10449
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10449}=\sqrt{81*129}=\sqrt{81}*\sqrt{129}=9\sqrt{129}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-117)-9\sqrt{129}}{2*1}=\frac{117-9\sqrt{129}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-117)+9\sqrt{129}}{2*1}=\frac{117+9\sqrt{129}}{2} $
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