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:

240=(4+6)t+0.5(3+2)t2 2.5t210t+240=0 2.5t2+10t240=0  a=2.5;b=10;c=240 D=b24ac=10242.5(240)=2500 D>0  t1,2=b±D2a=10±25005 t1,2=10±505 t1,2=2±10 t1=8 t2=12   Factored form of the equation:  2.5(t8)(t+12)=0 240 = (4+6) * t + 0.5 * (3+2)*t^2 \ \\ -2.5t^2 -10t +240 =0 \ \\ 2.5t^2 +10t -240 =0 \ \\ \ \\ a=2.5; b=10; c=-240 \ \\ D = b^2 - 4ac = 10^2 - 4\cdot 2.5 \cdot (-240) = 2500 \ \\ D>0 \ \\ \ \\ t_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ -10 \pm \sqrt{ 2500 } }{ 5 } \ \\ t_{1,2} = \dfrac{ -10 \pm 50 }{ 5 } \ \\ t_{1,2} = -2 \pm 10 \ \\ t_{1} = 8 \ \\ t_{2} = -12 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 2.5 (t -8) (t +12) = 0 \ \\

Solution in text:

-2.5t2-10t+240=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 2500
D>0 ... The equation has two distinct real roots

t1 = 8
t2 = -12

P = {8; -12}