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5x(4x-17)=9
We move all terms to the left:
5x(4x-17)-(9)=0
We multiply parentheses
20x^2-85x-9=0
a = 20; b = -85; c = -9;
Δ = b2-4ac
Δ = -852-4·20·(-9)
Δ = 7945
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{-(-85)-\sqrt{7945}}{2*20}=\frac{85-\sqrt{7945}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+\sqrt{7945}}{2*20}=\frac{85+\sqrt{7945}}{40} $
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