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13x^2-7100x+420000=0
a = 13; b = -7100; c = +420000;
Δ = b2-4ac
Δ = -71002-4·13·420000
Δ = 28570000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{28570000}=\sqrt{10000*2857}=\sqrt{10000}*\sqrt{2857}=100\sqrt{2857}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7100)-100\sqrt{2857}}{2*13}=\frac{7100-100\sqrt{2857}}{26} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7100)+100\sqrt{2857}}{2*13}=\frac{7100+100\sqrt{2857}}{26} $
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