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5x^2+81x-126=0
a = 5; b = 81; c = -126;
Δ = b2-4ac
Δ = 812-4·5·(-126)
Δ = 9081
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9081}=\sqrt{9*1009}=\sqrt{9}*\sqrt{1009}=3\sqrt{1009}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-3\sqrt{1009}}{2*5}=\frac{-81-3\sqrt{1009}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+3\sqrt{1009}}{2*5}=\frac{-81+3\sqrt{1009}}{10} $
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