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:

(36)2+(q14)2=152 q228q+52=0  a=1;b=28;c=52 D=b24ac=2824152=576 D>0  q1,2=b±D2a=28±5762 q1,2=28±242 q1,2=14±12 q1=26 q2=2   Factored form of the equation:  (q26)(q2)=0 (-3-6)^2 +(q-14)^2 = 15^2 \ \\ q^2 -28q +52 =0 \ \\ \ \\ a=1; b=-28; c=52 \ \\ D = b^2 - 4ac = 28^2 - 4\cdot 1 \cdot 52 = 576 \ \\ D>0 \ \\ \ \\ q_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 28 \pm \sqrt{ 576 } }{ 2 } \ \\ q_{1,2} = \dfrac{ 28 \pm 24 }{ 2 } \ \\ q_{1,2} = 14 \pm 12 \ \\ q_{1} = 26 \ \\ q_{2} = 2 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (q -26) (q -2) = 0 \ \\

Solution in text:

q2-28q+52=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 576
D>0 ... The equation has two distinct real roots

q1 = 26
q2 = 2

P = {26; 2}