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:

2∗589=(4+4+(n−1)∗3)∗n −3n2−5n+1178=0 3n2+5n−1178=0  a=3;b=5;c=−1178 D=b2−4ac=52−4⋅3⋅(−1178)=14161 D>0  n1,2=−b±D2a=−5±141616 n1,2=−5±1196 n1,2=−0.833333±19.833333 n1=19 n2=−20.666666667   Factored form of the equation:  3(n−19)(n+20.666666667)=0 2*589 = (4+4+(n-1)*3)*n \ \\ -3n^2 -5n +1178 =0 \ \\ 3n^2 +5n -1178 =0 \ \\ \ \\ a=3; b=5; c=-1178 \ \\ D = b^2 - 4ac = 5^2 - 4 \cdot 3 \cdot (-1178) = 14161 \ \\ D>0 \ \\ \ \\ n_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ -5 \pm \sqrt{ 14161 } }{ 6 } \ \\ n_{1,2} = \dfrac{ -5 \pm 119 }{ 6 } \ \\ n_{1,2} = -0.833333 \pm 19.833333 \ \\ n_{1} = 19 \ \\ n_{2} = -20.666666667 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 3 (n -19) (n +20.666666667) = 0 \ \\

Solution in text:

-3n2-5n+1178=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 14161
D > 0 ... The equation has two distinct real roots

n1 = 19
n2 = -20.6666667

P = {19; -20.6666667}