Mister Exam

# (8-2x)(6-x)-30=0 equation

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#### Numerical solution:

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### The solution

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(8 - 2*x)*(6 - x) - 30 = 0
$$\left(- x + 6\right) \left(- 2 x + 8\right) - 30 = 0$$
Detail solution
Expand the expression in the equation
$$\left(\left(- x + 6\right) \left(- 2 x + 8\right) - 30\right) + 0 = 0$$
$$2 x^{2} - 20 x + 18 = 0$$
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:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 2$$
$$b = -20$$
$$c = 18$$
, then
$$D = b^2 - 4\ a\ c =$$
$$\left(-1\right) 2 \cdot 4 \cdot 18 + \left(-20\right)^{2} = 256$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 9$$
Simplify
$$x_{2} = 1$$
Simplify
The graph
Sum and product of roots [src]
sum
1 + 9
$$\left(1\right) + \left(9\right)$$
=
10
$$10$$
product
1 * 9
$$\left(1\right) * \left(9\right)$$
=
9
$$9$$
Rapid solution [src]
x_1 = 1
$$x_{1} = 1$$
x_2 = 9
$$x_{2} = 9$$
x1 = 9.0
x2 = 1.0
x2 = 1.0