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10x^2+80x-40=0
a = 10; b = 80; c = -40;
Δ = b2-4ac
Δ = 802-4·10·(-40)
Δ = 8000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-40\sqrt{5}}{2*10}=\frac{-80-40\sqrt{5}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+40\sqrt{5}}{2*10}=\frac{-80+40\sqrt{5}}{20} $
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