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-10x^2+20x+17=0
a = -10; b = 20; c = +17;
Δ = b2-4ac
Δ = 202-4·(-10)·17
Δ = 1080
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-6\sqrt{30}}{2*-10}=\frac{-20-6\sqrt{30}}{-20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+6\sqrt{30}}{2*-10}=\frac{-20+6\sqrt{30}}{-20} $
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