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6x^2-25x=21
We move all terms to the left:
6x^2-25x-(21)=0
a = 6; b = -25; c = -21;
Δ = b2-4ac
Δ = -252-4·6·(-21)
Δ = 1129
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-\sqrt{1129}}{2*6}=\frac{25-\sqrt{1129}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{1129}}{2*6}=\frac{25+\sqrt{1129}}{12} $
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