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5x^2-34x-161=0
a = 5; b = -34; c = -161;
Δ = b2-4ac
Δ = -342-4·5·(-161)
Δ = 4376
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4376}=\sqrt{4*1094}=\sqrt{4}*\sqrt{1094}=2\sqrt{1094}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{1094}}{2*5}=\frac{34-2\sqrt{1094}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{1094}}{2*5}=\frac{34+2\sqrt{1094}}{10} $
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