Quadratic equation

Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.

Result

x1 =  2
x2 =  -0.667

Solution:

 3x24x+(4)=0 3x24x4=0  a=3;b=4;c=4 D=b24ac=4243(4)=64 D>0  x1,2=b±D2a=4±646 x1,2=4±86 x1,2=0.66666667±1.3333333333333 x1=2 x2=0.66666666666667   Factored form of the equation:  3(x2)(x+0.66666666666667)=0 x1=2 \ \\ 3x^2-4x+(-4)=0 \ \\ 3x^2 -4x -4=0 \ \\ \ \\ a=3; b=-4; c=-4 \ \\ D=b^2 - 4ac=4^2 - 4\cdot 3 \cdot (-4)=64 \ \\ D>0 \ \\ \ \\ x_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ 4 \pm \sqrt{ 64 } }{ 6 } \ \\ x_{1,2}=\dfrac{ 4 \pm 8 }{ 6 } \ \\ x_{1,2}=0.66666667 \pm 1.3333333333333 \ \\ x_{1}=2 \ \\ x_{2}=-0.66666666666667 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 3 (x -2) (x +0.66666666666667)=0 \ \\ x_{1}=2

Checkout calculation with our calculator of quadratic equations.

x2=(0.6667)=230.66670.667x_{2}=(-0.6667)=- \dfrac{ 2 }{ 3 } \doteq -0.6667 \doteq -0.667



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