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x^2-100x+1375=0
a = 1; b = -100; c = +1375;
Δ = b2-4ac
Δ = -1002-4·1·1375
Δ = 4500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-30\sqrt{5}}{2*1}=\frac{100-30\sqrt{5}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+30\sqrt{5}}{2*1}=\frac{100+30\sqrt{5}}{2} $
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