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(8x-11)*(-5x+17)=0 equation
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The solution
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[src]
(8*x - 11)*(-5*x + 17) = 0
$$\left(17 - 5 x\right) \left(8 x - 11\right) = 0$$
Detail solution
Expand the expression in the equation
$$\left(17 - 5 x\right) \left(8 x - 11\right) = 0$$
We get the quadratic equation
$$- 40 x^{2} + 191 x - 187 = 0$$
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
$$a = -40$$
$$b = 191$$
$$c = -187$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{11}{8}$$
$$x_{2} = \frac{17}{5}$$
$$\left(17 - 5 x\right) \left(8 x - 11\right) = 0$$
We get the quadratic equation
$$- 40 x^{2} + 191 x - 187 = 0$$
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
$$a = -40$$
$$b = 191$$
$$c = -187$$
, then
D = b^2 - 4 * a * c =
(191)^2 - 4 * (-40) * (-187) = 6561
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{11}{8}$$
$$x_{2} = \frac{17}{5}$$
Sum and product of roots
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sum
11/8 + 17/5
$$\frac{11}{8} + \frac{17}{5}$$
=
191 --- 40
$$\frac{191}{40}$$
product
11*17 ----- 8*5
$$\frac{11 \cdot 17}{5 \cdot 8}$$
=
187 --- 40
$$\frac{187}{40}$$
187/40
Rapid solution
[src]
x1 = 11/8
$$x_{1} = \frac{11}{8}$$
x2 = 17/5
$$x_{2} = \frac{17}{5}$$
x2 = 17/5