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6x^2+84x+22=0
a = 6; b = 84; c = +22;
Δ = b2-4ac
Δ = 842-4·6·22
Δ = 6528
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6528}=\sqrt{64*102}=\sqrt{64}*\sqrt{102}=8\sqrt{102}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-8\sqrt{102}}{2*6}=\frac{-84-8\sqrt{102}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+8\sqrt{102}}{2*6}=\frac{-84+8\sqrt{102}}{12} $
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