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:

1.232+(1.23+d)2=(1.23+2∗d)2 −3d2−2.46d+1.513=0 3d2+2.46d−1.513=0  a=3;b=2.46;c=−1.513 D=b2−4ac=2.462−4⋅3⋅(−1.513)=24.2064 D>0  d1,2=−b±D2a=−2.46±24.216 d1,2=−0.41±0.82 d1=0.41 d2=−1.23   Factored form of the equation:  3(d−0.41)(d+1.23)=0 1.23^2 + (1.23+d)^2 = (1.23+2*d)^2 \ \\ -3d^2 -2.46d +1.513 =0 \ \\ 3d^2 +2.46d -1.513 =0 \ \\ \ \\ a=3; b=2.46; c=-1.513 \ \\ D = b^2 - 4ac = 2.46^2 - 4 \cdot 3 \cdot (-1.513) = 24.2064 \ \\ D>0 \ \\ \ \\ d_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ -2.46 \pm \sqrt{ 24.21 } }{ 6 } \ \\ d_{1,2} = -0.41 \pm 0.82 \ \\ d_{1} = 0.41 \ \\ d_{2} = -1.23 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 3 (d -0.41) (d +1.23) = 0 \ \\

Solution in text:

-3d2-2.46d+1.5129=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 24.2064
D > 0 ... The equation has two distinct real roots

d1 = 0.41
d2 = -1.23

P = {0.41; -1.23}