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16x^2+100x+5=0
a = 16; b = 100; c = +5;
Δ = b2-4ac
Δ = 1002-4·16·5
Δ = 9680
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9680}=\sqrt{1936*5}=\sqrt{1936}*\sqrt{5}=44\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-44\sqrt{5}}{2*16}=\frac{-100-44\sqrt{5}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+44\sqrt{5}}{2*16}=\frac{-100+44\sqrt{5}}{32} $
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