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3x^2+2x-460=0
a = 3; b = 2; c = -460;
Δ = b2-4ac
Δ = 22-4·3·(-460)
Δ = 5524
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5524}=\sqrt{4*1381}=\sqrt{4}*\sqrt{1381}=2\sqrt{1381}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{1381}}{2*3}=\frac{-2-2\sqrt{1381}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{1381}}{2*3}=\frac{-2+2\sqrt{1381}}{6} $
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