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8x^2+84x+3=0
a = 8; b = 84; c = +3;
Δ = b2-4ac
Δ = 842-4·8·3
Δ = 6960
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6960}=\sqrt{16*435}=\sqrt{16}*\sqrt{435}=4\sqrt{435}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{435}}{2*8}=\frac{-84-4\sqrt{435}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{435}}{2*8}=\frac{-84+4\sqrt{435}}{16} $
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