Mister Exam
(3x+42)(4,8-0,6x)=0 equation
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The solution
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[src]
/24 3*x\
(3*x + 42)*|-- - ---| = 0
\5 5 /
$$\left(\frac{24}{5} - \frac{3 x}{5}\right) \left(3 x + 42\right) = 0$$
Detail solution
Expand the expression in the equation
$$\left(\frac{24}{5} - \frac{3 x}{5}\right) \left(3 x + 42\right) = 0$$
We get the quadratic equation
$$- \frac{9 x^{2}}{5} - \frac{54 x}{5} + \frac{1008}{5} = 0$$
This equation is of the form
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 - it is the discriminant.
Because
$$a = - \frac{9}{5}$$
$$b = - \frac{54}{5}$$
$$c = \frac{1008}{5}$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -14$$
$$x_{2} = 8$$
$$\left(\frac{24}{5} - \frac{3 x}{5}\right) \left(3 x + 42\right) = 0$$
We get the quadratic equation
$$- \frac{9 x^{2}}{5} - \frac{54 x}{5} + \frac{1008}{5} = 0$$
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 - it is the discriminant.
Because
$$a = - \frac{9}{5}$$
$$b = - \frac{54}{5}$$
$$c = \frac{1008}{5}$$
, then
D = b^2 - 4 * a * c =
(-54/5)^2 - 4 * (-9/5) * (1008/5) = 39204/25
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -14$$
$$x_{2} = 8$$
Sum and product of roots
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sum
-14 + 8
$$-14 + 8$$
=
-6
$$-6$$
product
-14*8
$$- 112$$
=
-112
$$-112$$
-112