Quadratic equation calculator

Quadratic equation has the basic form:
ax2+bx+c=0ax^2+bx+c=0

eq2
Enter the coefficients a, b, c of quadratic equation in 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:

8(x6)+8x=(x6)x x2+22x48=0 x222x+48=0  a=1;b=22;c=48 D=b24ac=2224148=292 D>0  x1,2=b±D2a=22±2922=22±2732 x1,2=11±8.54400374532 x1=19.5440037453 x2=2.45599625468   Factored form of the equation:  (x19.5440037453)(x2.45599625468)=08*(x-6) + 8*x = (x-6) * x \ \\ -x^2 +22x -48 =0 \ \\ x^2 -22x +48 =0 \ \\ \ \\ a=1; b=-22; c=48 \ \\ D = b^2 - 4ac = 22^2 - 4\cdot 1 \cdot 48 = 292 \ \\ D>0 \ \\ \ \\ x_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 22 \pm \sqrt{ 292 } }{ 2 } = \dfrac{ 22 \pm 2 \sqrt{ 73 } }{ 2 } \ \\ x_{1,2} = 11 \pm 8.54400374532 \ \\ x_{1} = 19.5440037453 \ \\ x_{2} = 2.45599625468 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -19.5440037453) (x -2.45599625468) = 0

Solution in text:

-x2+22x-48=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 292
D>0 ... The equation has two distinct real roots

x1 = 19.5440037453
x2 = 2.45599625468

P = {19.5440037453; 2.45599625468}