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2x(x-3)+3x=14
We move all terms to the left:
2x(x-3)+3x-(14)=0
We add all the numbers together, and all the variables
3x+2x(x-3)-14=0
We multiply parentheses
2x^2+3x-6x-14=0
We add all the numbers together, and all the variables
2x^2-3x-14=0
a = 2; b = -3; c = -14;
Δ = b2-4ac
Δ = -32-4·2·(-14)
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-11}{2*2}=\frac{-8}{4} =-2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+11}{2*2}=\frac{14}{4} =3+1/2 $
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