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:

n(n+10)=200 n2+10n−200=0  a=1;b=10;c=−200 D=b2−4ac=102−4⋅1⋅(−200)=900 D>0  n1,2=−b±D2a=−10±9002 n1,2=−10±302 n1,2=−5±15 n1=10 n2=−20   Factored form of the equation:  (n−10)(n+20)=0 n(n+10)=200 \ \\ n^2 +10n -200 =0 \ \\ \ \\ a=1; b=10; c=-200 \ \\ D = b^2 - 4ac = 10^2 - 4 \cdot 1 \cdot (-200) = 900 \ \\ D>0 \ \\ \ \\ n_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ -10 \pm \sqrt{ 900 } }{ 2 } \ \\ n_{1,2} = \dfrac{ -10 \pm 30 }{ 2 } \ \\ n_{1,2} = -5 \pm 15 \ \\ n_{1} = 10 \ \\ n_{2} = -20 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (n -10) (n +20) = 0 \ \\

Solution in text:

n2+10n-200=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 900
D > 0 ... The equation has two distinct real roots

n1 = 10
n2 = -20

P = {10; -20}