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-25x^2+5x+10=0
a = -25; b = 5; c = +10;
Δ = b2-4ac
Δ = 52-4·(-25)·10
Δ = 1025
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{41}}{2*-25}=\frac{-5-5\sqrt{41}}{-50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{41}}{2*-25}=\frac{-5+5\sqrt{41}}{-50} $
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