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:

(x+2)(x3)=24 x2x30=0  a=1;b=1;c=30 D=b24ac=1241(30)=121 D>0  x1,2=b±D2a=1±1212 x1,2=1±112 x1,2=0.5±5.5 x1=6 x2=5   Factored form of the equation:  (x6)(x+5)=0 (x+2)(x-3)=24 \ \\ x^2 -x -30 =0 \ \\ \ \\ a=1; b=-1; c=-30 \ \\ D = b^2 - 4ac = 1^2 - 4 \cdot 1 \cdot (-30) = 121 \ \\ D>0 \ \\ \ \\ x_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 1 \pm \sqrt{ 121 } }{ 2 } \ \\ x_{1,2} = \dfrac{ 1 \pm 11 }{ 2 } \ \\ x_{1,2} = 0.5 \pm 5.5 \ \\ x_{1} = 6 \ \\ x_{2} = -5 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -6) (x +5) = 0 \ \\

Solution in text:

x2-x-30=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 121
D > 0 ... The equation has two distinct real roots

x1 = 6
x2 = -5

P = {6; -5}