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:

302=a2+(42−a)2 −2a2+84a−864=0 2a2−84a+864=0 2 ...  prime number 84=22⋅3⋅7 864=25⋅33 GCD(2,84,864)=2=2  a2−42a+432=0  p=1;q=−42;r=432 D=q2−4pr=422−4⋅1⋅432=36 D>0  a1,2=−q±D2p=42±362 a1,2=42±62 a1,2=21±3 a1=24 a2=18   Factored form of the equation:  (a−24)(a−18)=0 30^2 = a^2 + (42-a)^2 \ \\ -2a^2 +84a -864 =0 \ \\ 2a^2 -84a +864 =0 \ \\ 2 \ ... \ \text{ prime number} \ \\ 84 = 2^2 \cdot 3 \cdot 7 \ \\ 864 = 2^5 \cdot 3^3 \ \\ \text{GCD}(2, 84, 864) = 2 = 2 \ \\ \ \\ a^2 -42a +432 =0 \ \\ \ \\ p=1; q=-42; r=432 \ \\ D = q^2 - 4pr = 42^2 - 4 \cdot 1 \cdot 432 = 36 \ \\ D>0 \ \\ \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ 42 \pm \sqrt{ 36 } }{ 2 } \ \\ a_{1,2} = \dfrac{ 42 \pm 6 }{ 2 } \ \\ a_{1,2} = 21 \pm 3 \ \\ a_{1} = 24 \ \\ a_{2} = 18 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (a -24) (a -18) = 0 \ \\

Solution in text:

-2a2+84a-864=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 144
D > 0 ... The equation has two distinct real roots

a1 = 24
a2 = 18

P = {24; 18}