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3x(4x+6)=84
We move all terms to the left:
3x(4x+6)-(84)=0
We multiply parentheses
12x^2+18x-84=0
a = 12; b = 18; c = -84;
Δ = b2-4ac
Δ = 182-4·12·(-84)
Δ = 4356
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{4356}=66$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-66}{2*12}=\frac{-84}{24} =-3+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+66}{2*12}=\frac{48}{24} =2 $
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