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:

3300=36∗n+n/2∗(n−1)∗4 −2n2−34n+3300=0 2n2+34n−3300=0 2 ...  prime number 34=2⋅17 3300=22⋅3⋅52⋅11 GCD(2,34,3300)=2=2  n2+17n−1650=0  a=1;b=17;c=−1650 D=b2−4ac=172−4⋅1⋅(−1650)=6889 D>0  n1,2=−b±D2a=−17±68892 n1,2=−17±832 n1,2=−8.5±41.5 n1=33 n2=−50   Factored form of the equation:  (n−33)(n+50)=0 3300 = 36*n + n/2 * (n-1) *4 \ \\ -2n^2 -34n +3300 =0 \ \\ 2n^2 +34n -3300 =0 \ \\ 2 \ ... \ \text{ prime number} \ \\ 34 = 2 \cdot 17 \ \\ 3300 = 2^2 \cdot 3 \cdot 5^2 \cdot 11 \ \\ \text{GCD}(2, 34, 3300) = 2 = 2 \ \\ \ \\ n^2 +17n -1650 =0 \ \\ \ \\ a=1; b=17; c=-1650 \ \\ D = b^2 - 4ac = 17^2 - 4 \cdot 1 \cdot (-1650) = 6889 \ \\ D>0 \ \\ \ \\ n_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ -17 \pm \sqrt{ 6889 } }{ 2 } \ \\ n_{1,2} = \dfrac{ -17 \pm 83 }{ 2 } \ \\ n_{1,2} = -8.5 \pm 41.5 \ \\ n_{1} = 33 \ \\ n_{2} = -50 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (n -33) (n +50) = 0 \ \\

Solution in text:

-2n2-34n+3300=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 27556
D > 0 ... The equation has two distinct real roots

n1 = 33
n2 = -50

P = {33; -50}