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x^2-145x+160=0
a = 1; b = -145; c = +160;
Δ = b2-4ac
Δ = -1452-4·1·160
Δ = 20385
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20385}=\sqrt{9*2265}=\sqrt{9}*\sqrt{2265}=3\sqrt{2265}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-145)-3\sqrt{2265}}{2*1}=\frac{145-3\sqrt{2265}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-145)+3\sqrt{2265}}{2*1}=\frac{145+3\sqrt{2265}}{2} $
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