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:

a23/4a20=990 a215a990=0  p=1;q=15;r=990 D=q24pr=15241(990)=4185 D>0  a1,2=q±D2p=15±41852=15±34652 a1,2=7.5±32.345787979272 a1=39.845787979272 a2=24.845787979272   Factored form of the equation:  (a39.845787979272)(a+24.845787979272)=0 a^2 - 3/4*a*20 = 990 \ \\ a^2 -15a -990 =0 \ \\ \ \\ p=1; q=-15; r=-990 \ \\ D = q^2 - 4pr = 15^2 - 4\cdot 1 \cdot (-990) = 4185 \ \\ D>0 \ \\ \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ 15 \pm \sqrt{ 4185 } }{ 2 } = \dfrac{ 15 \pm 3 \sqrt{ 465 } }{ 2 } \ \\ a_{1,2} = 7.5 \pm 32.345787979272 \ \\ a_{1} = 39.845787979272 \ \\ a_{2} = -24.845787979272 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (a -39.845787979272) (a +24.845787979272) = 0 \ \\

Solution in text:

a2-15a-990=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 4185
D>0 ... The equation has two distinct real roots

a1 = 39.845787979272
a2 = -24.845787979272

P = {39.845787979272; -24.845787979272}