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3x(2x+3)+4x+2=21
We move all terms to the left:
3x(2x+3)+4x+2-(21)=0
We add all the numbers together, and all the variables
4x+3x(2x+3)-19=0
We multiply parentheses
6x^2+4x+9x-19=0
We add all the numbers together, and all the variables
6x^2+13x-19=0
a = 6; b = 13; c = -19;
Δ = b2-4ac
Δ = 132-4·6·(-19)
Δ = 625
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{625}=25$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-25}{2*6}=\frac{-38}{12} =-3+1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+25}{2*6}=\frac{12}{12} =1 $
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