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6x(4x+3)=690
We move all terms to the left:
6x(4x+3)-(690)=0
We multiply parentheses
24x^2+18x-690=0
a = 24; b = 18; c = -690;
Δ = b2-4ac
Δ = 182-4·24·(-690)
Δ = 66564
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{66564}=258$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-258}{2*24}=\frac{-276}{48} =-5+3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+258}{2*24}=\frac{240}{48} =5 $
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