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:

15a2+75a+125=485 15a2+75a−360=0 15=3⋅5 75=3⋅52 360=23⋅32⋅5 GCD(15,75,360)=3⋅5=15  a2+5a−24=0  p=1;q=5;r=−24 D=q2−4pr=52−4⋅1⋅(−24)=121 D>0  a1,2=−q±D2p=−5±1212 a1,2=−5±112 a1,2=−2.5±5.5 a1=3 a2=−8   Factored form of the equation:  (a−3)(a+8)=0 15 a^2 + 75 a + 125 = 485 \ \\ 15a^2 +75a -360 =0 \ \\ 15 = 3 \cdot 5 \ \\ 75 = 3 \cdot 5^2 \ \\ 360 = 2^3 \cdot 3^2 \cdot 5 \ \\ \text{GCD}(15, 75, 360) = 3 \cdot 5 = 15 \ \\ \ \\ a^2 +5a -24 =0 \ \\ \ \\ p=1; q=5; r=-24 \ \\ D = q^2 - 4pr = 5^2 - 4 \cdot 1 \cdot (-24) = 121 \ \\ D>0 \ \\ \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ -5 \pm \sqrt{ 121 } }{ 2 } \ \\ a_{1,2} = \dfrac{ -5 \pm 11 }{ 2 } \ \\ a_{1,2} = -2.5 \pm 5.5 \ \\ a_{1} = 3 \ \\ a_{2} = -8 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (a -3) (a +8) = 0 \ \\

Solution in text:

15a2+75a-360=0 ... quadratic equation

Discriminant:
D = b2 - 4ac = 27225
D > 0 ... The equation has two distinct real roots

a1 = 3
a2 = -8

P = {3; -8}