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6x^2+39x=60
We move all terms to the left:
6x^2+39x-(60)=0
a = 6; b = 39; c = -60;
Δ = b2-4ac
Δ = 392-4·6·(-60)
Δ = 2961
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2961}=\sqrt{9*329}=\sqrt{9}*\sqrt{329}=3\sqrt{329}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3\sqrt{329}}{2*6}=\frac{-39-3\sqrt{329}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3\sqrt{329}}{2*6}=\frac{-39+3\sqrt{329}}{12} $
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