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:

b2b12=0 b2b12=0  p=1;q=1;r=12 D=q24pr=1241(12)=49 D>0  b1,2=q±D2p=1±492 b1,2=1±72 b1,2=0.5±3.5 b1=4 b2=3   Factored form of the equation:  (b4)(b+3)=0 b^2-b-12=0 \ \\ b^2 -b -12 =0 \ \\ \ \\ p=1; q=-1; r=-12 \ \\ D = q^2 - 4pr = 1^2 - 4\cdot 1 \cdot (-12) = 49 \ \\ D>0 \ \\ \ \\ b_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ 1 \pm \sqrt{ 49 } }{ 2 } \ \\ b_{1,2} = \dfrac{ 1 \pm 7 }{ 2 } \ \\ b_{1,2} = 0.5 \pm 3.5 \ \\ b_{1} = 4 \ \\ b_{2} = -3 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (b -4) (b +3) = 0 \ \\

Solution in text:

b2-b-12=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 49
D>0 ... The equation has two distinct real roots

b1 = 4
b2 = -3

P = {4; -3}