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5x^2-41x=66
We move all terms to the left:
5x^2-41x-(66)=0
a = 5; b = -41; c = -66;
Δ = b2-4ac
Δ = -412-4·5·(-66)
Δ = 3001
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-\sqrt{3001}}{2*5}=\frac{41-\sqrt{3001}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{3001}}{2*5}=\frac{41+\sqrt{3001}}{10} $
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