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:

h(h2)=84 h22h84=0  a=1;b=2;c=84 D=b24ac=2241(84)=340 D>0  h1,2=b±D2a=2±3402=2±2852 h1,2=1±9.21954445729 h1=10.2195444573 h2=8.21954445729   Factored form of the equation:  (h10.2195444573)(h+8.21954445729)=0 h(h-2) = 84 \ \\ h^2 -2h -84 =0 \ \\ \ \\ a=1; b=-2; c=-84 \ \\ D = b^2 - 4ac = 2^2 - 4\cdot 1 \cdot (-84) = 340 \ \\ D>0 \ \\ \ \\ h_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 2 \pm \sqrt{ 340 } }{ 2 } = \dfrac{ 2 \pm 2 \sqrt{ 85 } }{ 2 } \ \\ h_{1,2} = 1 \pm 9.21954445729 \ \\ h_{1} = 10.2195444573 \ \\ h_{2} = -8.21954445729 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (h -10.2195444573) (h +8.21954445729) = 0 \ \\

Solution in text:

h2-2h-84=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 340
D>0 ... The equation has two distinct real roots

h1 = 10.2195444573
h2 = -8.21954445729

P = {10.2195444573; -8.21954445729}