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5x^2+25x-10=0
a = 5; b = 25; c = -10;
Δ = b2-4ac
Δ = 252-4·5·(-10)
Δ = 825
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{33}}{2*5}=\frac{-25-5\sqrt{33}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{33}}{2*5}=\frac{-25+5\sqrt{33}}{10} $
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