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29x^2+91x-84=0
a = 29; b = 91; c = -84;
Δ = b2-4ac
Δ = 912-4·29·(-84)
Δ = 18025
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{18025}=\sqrt{25*721}=\sqrt{25}*\sqrt{721}=5\sqrt{721}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(91)-5\sqrt{721}}{2*29}=\frac{-91-5\sqrt{721}}{58} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+5\sqrt{721}}{2*29}=\frac{-91+5\sqrt{721}}{58} $
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