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:

50b=2b2+20b+220 2b2+30b40=0 2b230b+40=0 2 ...  prime number 30=235 40=235 GCD(2,30,40)=2=2  b215b+20=0  p=1;q=15;r=20 D=q24pr=1524120=145 D>0  b1,2=2pq±D=215±145 b1,2=7.5±6.020797 b1=13.520797289 b2=1.479202711   Factored form of the equation:  (b13.520797289)(b1.479202711)=0 

Solution in text:

-2b2+30b-40=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 580
D > 0 ... The equation has two distinct real roots

b1 = 13.5207973
b2 = 1.4792027

P = {13.5207973; 1.4792027}