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175+78x+6x^2=0
a = 6; b = 78; c = +175;
Δ = b2-4ac
Δ = 782-4·6·175
Δ = 1884
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1884}=\sqrt{4*471}=\sqrt{4}*\sqrt{471}=2\sqrt{471}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{471}}{2*6}=\frac{-78-2\sqrt{471}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{471}}{2*6}=\frac{-78+2\sqrt{471}}{12} $
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