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5x^2-54x-170=0
a = 5; b = -54; c = -170;
Δ = b2-4ac
Δ = -542-4·5·(-170)
Δ = 6316
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6316}=\sqrt{4*1579}=\sqrt{4}*\sqrt{1579}=2\sqrt{1579}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{1579}}{2*5}=\frac{54-2\sqrt{1579}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{1579}}{2*5}=\frac{54+2\sqrt{1579}}{10} $
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