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:

2a2−46a+240=0 2a2−46a+240=0 2 ...  prime number 46=2⋅23 240=24⋅3⋅5 GCD(2,46,240)=2=2  a2−23a+120=0  p=1;q=−23;r=120 D=q2−4pr=232−4⋅1⋅120=49 D>0  a1,2=−q±D2p=23±492 a1,2=23±72 a1,2=11.5±3.5 a1=15 a2=8   Factored form of the equation:  (a−15)(a−8)=0 2a^2 - 46a +240 = 0 \ \\ 2a^2 -46a +240 =0 \ \\ 2 \ ... \ \text{ prime number} \ \\ 46 = 2 \cdot 23 \ \\ 240 = 2^4 \cdot 3 \cdot 5 \ \\ \text{GCD}(2, 46, 240) = 2 = 2 \ \\ \ \\ a^2 -23a +120 =0 \ \\ \ \\ p=1; q=-23; r=120 \ \\ D = q^2 - 4pr = 23^2 - 4 \cdot 1 \cdot 120 = 49 \ \\ D>0 \ \\ \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ 23 \pm \sqrt{ 49 } }{ 2 } \ \\ a_{1,2} = \dfrac{ 23 \pm 7 }{ 2 } \ \\ a_{1,2} = 11.5 \pm 3.5 \ \\ a_{1} = 15 \ \\ a_{2} = 8 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (a -15) (a -8) = 0 \ \\

Solution in text:

2a2-46a+240=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 196
D > 0 ... The equation has two distinct real roots

a1 = 15
a2 = 8

P = {15; 8}