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:

165000=n∣2∗(2∗4000+(n−1)∗1000) −500n2−3500n+165000=0 500n2+3500n−165000=0 500=22⋅53 3500=22⋅53⋅7 165000=23⋅3⋅54⋅11 GCD(500,3500,165000)=22⋅53=500  n2+7n−330=0  a=1;b=7;c=−330 D=b2−4ac=72−4⋅1⋅(−330)=1369 D>0  n1,2=−b±D2a=−7±13692 n1,2=−7±372 n1,2=−3.5±18.5 n1=15 n2=−22   Factored form of the equation:  (n−15)(n+22)=0 165000 = n|2 * (2*4000+(n-1)*1000) \ \\ -500n^2 -3500n +165000 =0 \ \\ 500n^2 +3500n -165000 =0 \ \\ 500 = 2^2 \cdot 5^3 \ \\ 3500 = 2^2 \cdot 5^3 \cdot 7 \ \\ 165000 = 2^3 \cdot 3 \cdot 5^4 \cdot 11 \ \\ \text{GCD}(500, 3500, 165000) = 2^2 \cdot 5^3 = 500 \ \\ \ \\ n^2 +7n -330 =0 \ \\ \ \\ a=1; b=7; c=-330 \ \\ D = b^2 - 4ac = 7^2 - 4 \cdot 1 \cdot (-330) = 1369 \ \\ D>0 \ \\ \ \\ n_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ -7 \pm \sqrt{ 1369 } }{ 2 } \ \\ n_{1,2} = \dfrac{ -7 \pm 37 }{ 2 } \ \\ n_{1,2} = -3.5 \pm 18.5 \ \\ n_{1} = 15 \ \\ n_{2} = -22 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (n -15) (n +22) = 0 \ \\

Solution in text:

-500n2-3500n+165000=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 342250000
D > 0 ... The equation has two distinct real roots

n1 = 15
n2 = -22

P = {15; -22}