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:

1+r=6∗r2 −6r2+r+1=0 6r2−r−1=0  a=6;b=−1;c=−1 D=b2−4ac=12−4⋅6⋅(−1)=25 D>0  r1,2=−b±D2a=1±2512 r1,2=1±512 r1,2=0.083333±0.416667 r1=0.5 r2=−0.333333333   Factored form of the equation:  6(r−0.5)(r+0.333333333)=0 1 + r = 6*r^2 \ \\ -6r^2 +r +1 =0 \ \\ 6r^2 -r -1 =0 \ \\ \ \\ a=6; b=-1; c=-1 \ \\ D = b^2 - 4ac = 1^2 - 4 \cdot 6 \cdot (-1) = 25 \ \\ D>0 \ \\ \ \\ r_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 1 \pm \sqrt{ 25 } }{ 12 } \ \\ r_{1,2} = \dfrac{ 1 \pm 5 }{ 12 } \ \\ r_{1,2} = 0.083333 \pm 0.416667 \ \\ r_{1} = 0.5 \ \\ r_{2} = -0.333333333 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 6 (r -0.5) (r +0.333333333) = 0 \ \\

Solution in text:

-6r2+r+1=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 25
D > 0 ... The equation has two distinct real roots

r1 = 0.5
r2 = -0.3333333

P = {0.5; -0.3333333}