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6x^2-30x=84
We move all terms to the left:
6x^2-30x-(84)=0
a = 6; b = -30; c = -84;
Δ = b2-4ac
Δ = -302-4·6·(-84)
Δ = 2916
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{2916}=54$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-54}{2*6}=\frac{-24}{12} =-2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+54}{2*6}=\frac{84}{12} =7 $
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