Quadratic equation calculator

Quadratic equation has the basic form: ax2+bx+c=0
eq2
Enter the quadratic equation's coefficients a, b, and c of its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant.


Calculation:

100∗(x−21)=x2 −x2+100x−2100=0 x2−100x+2100=0  a=1;b=−100;c=2100 D=b2−4ac=1002−4⋅1⋅2100=1600 D>0  x1,2=−b±D2a=100±16002 x1,2=100±402 x1,2=50±20 x1=70 x2=30   Factored form of the equation:  (x−70)(x−30)=0 100*(x-21)=x^2 \ \\ -x^2 +100x -2100 =0 \ \\ x^2 -100x +2100 =0 \ \\ \ \\ a=1; b=-100; c=2100 \ \\ D = b^2 - 4ac = 100^2 - 4 \cdot 1 \cdot 2100 = 1600 \ \\ D>0 \ \\ \ \\ x_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 100 \pm \sqrt{ 1600 } }{ 2 } \ \\ x_{1,2} = \dfrac{ 100 \pm 40 }{ 2 } \ \\ x_{1,2} = 50 \pm 20 \ \\ x_{1} = 70 \ \\ x_{2} = 30 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -70) (x -30) = 0 \ \\

Solution in text:

-x2+100x-2100=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 1600
D > 0 ... The equation has two distinct real roots

x1 = 70
x2 = 30

P = {70; 30}