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3x^2-75=0 equation

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Numerical solution:

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3*x  - 75 = 0
3x2−75=03 x^{2} - 75 = 0
Simplify
Detail solution
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=3a = 3
b=0b = 0
c=−75c = -75
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (3) * (-75) = 900

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
x1=5x_{1} = 5
Simplify
x2=−5x_{2} = -5
Simplify
Vieta's Theorem
rewrite the equation
3x2−75=03 x^{2} - 75 = 0
of
ax2+bx+c=0a x^{2} + b x + c = 0
as reduced quadratic equation
x2+bxa+ca=0x^{2} + \frac{b x}{a} + \frac{c}{a} = 0
x2−25=0x^{2} - 25 = 0
px+x2+q=0p x + x^{2} + q = 0
where
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=−25q = -25
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=0x_{1} + x_{2} = 0
x1x2=−25x_{1} x_{2} = -25
Rapid solution [src] 
x1 = -5
x1=−5x_{1} = -5
Simplify 
x2 = 5
x2=5x_{2} = 5
Simplify
Sum and product of roots [src] 
sum
0 - 5 + 5
(−5+0)+5\left(-5 + 0\right) + 5 
=
0
00 
product
1*-5*5
1(−5)51 \left(-5\right) 5 
=
-25
−25-25 
-25
Numerical answer [src] 
x1 = 5.0
x2 = -5.0
x2 = -5.0
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