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:

140=3sqrt(3)a2+30a 5.1961524227066a230a+140=0 5.1961524227066a2+30a140=0  p=5.1961524227066;q=30;r=140 D=q24pr=30245.1961524227066(140)=3809.8453567157 D>0  a1,2=q±D2p=30±3809.8510.392304845413 a1,2=2.88675135±5.9393893537565 a1=3.0526380078084 a2=8.8261406997046   Factored form of the equation:  5.1961524227066(a3.0526380078084)(a+8.8261406997046)=0 140 = 3*sqrt(3)*a^2 + 30a \ \\ -5.1961524227066a^2 -30a +140 =0 \ \\ 5.1961524227066a^2 +30a -140 =0 \ \\ \ \\ p=5.1961524227066; q=30; r=-140 \ \\ D = q^2 - 4pr = 30^2 - 4\cdot 5.1961524227066 \cdot (-140) = 3809.8453567157 \ \\ D>0 \ \\ \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ -30 \pm \sqrt{ 3809.85 } }{ 10.392304845413 } \ \\ a_{1,2} = -2.88675135 \pm 5.9393893537565 \ \\ a_{1} = 3.0526380078084 \ \\ a_{2} = -8.8261406997046 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 5.1961524227066 (a -3.0526380078084) (a +8.8261406997046) = 0 \ \\

Solution in text:

-5.1961524227066a2-30a+140=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 3809.8453567157
D>0 ... The equation has two distinct real roots

a1 = 3.0526380078084
a2 = -8.8261406997046

P = {3.0526380078084; -8.8261406997046}