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5x^2-41x+66=0
a = 5; b = -41; c = +66;
Δ = b2-4ac
Δ = -412-4·5·66
Δ = 361
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{361}=19$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-19}{2*5}=\frac{22}{10} =2+1/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+19}{2*5}=\frac{60}{10} =6 $
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