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3x*(2x-5)=684
We move all terms to the left:
3x*(2x-5)-(684)=0
We multiply parentheses
6x^2-15x-684=0
a = 6; b = -15; c = -684;
Δ = b2-4ac
Δ = -152-4·6·(-684)
Δ = 16641
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{16641}=129$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-129}{2*6}=\frac{-114}{12} =-9+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+129}{2*6}=\frac{144}{12} =12 $
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