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:

(y−30)∗y=1000 y2−30y−1000=0  a=1;b=−30;c=−1000 D=b2−4ac=302−4⋅1⋅(−1000)=4900 D>0  y1,2=−b±D2a=30±49002 y1,2=30±702 y1,2=15±35 y1=50 y2=−20   Factored form of the equation:  (y−50)(y+20)=0 (y-30)*y=1000 \ \\ y^2 -30y -1000 =0 \ \\ \ \\ a=1; b=-30; c=-1000 \ \\ D = b^2 - 4ac = 30^2 - 4 \cdot 1 \cdot (-1000) = 4900 \ \\ D>0 \ \\ \ \\ y_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 30 \pm \sqrt{ 4900 } }{ 2 } \ \\ y_{1,2} = \dfrac{ 30 \pm 70 }{ 2 } \ \\ y_{1,2} = 15 \pm 35 \ \\ y_{1} = 50 \ \\ y_{2} = -20 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (y -50) (y +20) = 0 \ \\

Solution in text:

y2-30y-1000=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 4900
D > 0 ... The equation has two distinct real roots

y1 = 50
y2 = -20

P = {50; -20}