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:

(1002p)(100p)=100(10062.5) 2p2300p+6250=0  a=2;b=300;c=6250 D=b24ac=3002426250=40000 D>0  p1,2=b±D2a=300±400004 p1,2=300±2004 p1,2=75±50 p1=125 p2=25   Factored form of the equation:  2(p125)(p25)=0 (100-2p)*(100-p) = 100*(100 - 62.5) \ \\ 2p^2 -300p +6250 =0 \ \\ \ \\ a=2; b=-300; c=6250 \ \\ D = b^2 - 4ac = 300^2 - 4\cdot 2 \cdot 6250 = 40000 \ \\ D>0 \ \\ \ \\ p_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 300 \pm \sqrt{ 40000 } }{ 4 } \ \\ p_{1,2} = \dfrac{ 300 \pm 200 }{ 4 } \ \\ p_{1,2} = 75 \pm 50 \ \\ p_{1} = 125 \ \\ p_{2} = 25 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 2 (p -125) (p -25) = 0 \ \\

Solution in text:

2p2-300p+6250=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 40000
D>0 ... The equation has two distinct real roots

p1 = 125
p2 = 25

P = {125; 25}