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5x(3x-5)=17
We move all terms to the left:
5x(3x-5)-(17)=0
We multiply parentheses
15x^2-25x-17=0
a = 15; b = -25; c = -17;
Δ = b2-4ac
Δ = -252-4·15·(-17)
Δ = 1645
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{-(-25)-\sqrt{1645}}{2*15}=\frac{25-\sqrt{1645}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{1645}}{2*15}=\frac{25+\sqrt{1645}}{30} $
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