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16x^2-2025x+40500=0
a = 16; b = -2025; c = +40500;
Δ = b2-4ac
Δ = -20252-4·16·40500
Δ = 1508625
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1508625}=\sqrt{2025*745}=\sqrt{2025}*\sqrt{745}=45\sqrt{745}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2025)-45\sqrt{745}}{2*16}=\frac{2025-45\sqrt{745}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2025)+45\sqrt{745}}{2*16}=\frac{2025+45\sqrt{745}}{32} $
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