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-5x^2+17x+13=0
a = -5; b = 17; c = +13;
Δ = b2-4ac
Δ = 172-4·(-5)·13
Δ = 549
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{549}=\sqrt{9*61}=\sqrt{9}*\sqrt{61}=3\sqrt{61}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-3\sqrt{61}}{2*-5}=\frac{-17-3\sqrt{61}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+3\sqrt{61}}{2*-5}=\frac{-17+3\sqrt{61}}{-10} $
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