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:

108=(12+b)b b212b+108=0 b2+12b108=0  p=1;q=12;r=108 D=q24pr=12241(108)=576 D>0  b1,2=q±D2p=12±5762 b1,2=12±242 b1,2=6±12 b1=6 b2=18   Factored form of the equation:  (b6)(b+18)=0 108=(12+b)*b \ \\ -b^2 -12b +108 =0 \ \\ b^2 +12b -108 =0 \ \\ \ \\ p=1; q=12; r=-108 \ \\ D = q^2 - 4pr = 12^2 - 4 \cdot 1 \cdot (-108) = 576 \ \\ D>0 \ \\ \ \\ b_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ -12 \pm \sqrt{ 576 } }{ 2 } \ \\ b_{1,2} = \dfrac{ -12 \pm 24 }{ 2 } \ \\ b_{1,2} = -6 \pm 12 \ \\ b_{1} = 6 \ \\ b_{2} = -18 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (b -6) (b +18) = 0 \ \\

Solution in text:

-b2-12b+108=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 576
D > 0 ... The equation has two distinct real roots

b1 = 6
b2 = -18

P = {6; -18}