Quadratic equation calculator

Quadratic equation has the basic form:
ax2+bx+c=0ax^2+bx+c=0

eq2
Enter the coefficients a, b, c of quadratic equation in 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:

16875=a(600/2a) a2300a+16875=0  p=1;q=300;r=16875 D=q24pr=30024116875=22500 D>0  a1,2=q±D2p=300±225002 a1,2=300±1502 a1,2=150±75 a1=225 a2=75   Factored form of the equation:  (a225)(a75)=0 16875 = a*(600/2-a) \ \\ a^2 -300a +16875 =0 \ \\ \ \\ p=1; q=-300; r=16875 \ \\ D = q^2 - 4pr = 300^2 - 4\cdot 1 \cdot 16875 = 22500 \ \\ D>0 \ \\ \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ 300 \pm \sqrt{ 22500 } }{ 2 } \ \\ a_{1,2} = \dfrac{ 300 \pm 150 }{ 2 } \ \\ a_{1,2} = 150 \pm 75 \ \\ a_{1} = 225 \ \\ a_{2} = 75 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (a -225) (a -75) = 0 \ \\

Solution in text:

a2-300a+16875=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 22500
D>0 ... The equation has two distinct real roots

a1 = 225
a2 = 75

P = {225; 75}