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(x-1)(3x-15)-36=0 equation
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The solution
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(x - 1)*(3*x - 15) - 36 = 0
$$\left(x - 1\right) \left(3 x - 15\right) - 36 = 0$$
Detail solution
Expand the expression in the equation
$$\left(x - 1\right) \left(3 x - 15\right) - 36 = 0$$
We get the quadratic equation
$$3 x^{2} - 18 x - 21 = 0$$
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
$$a = 3$$
$$b = -18$$
$$c = -21$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 7$$
$$x_{2} = -1$$
$$\left(x - 1\right) \left(3 x - 15\right) - 36 = 0$$
We get the quadratic equation
$$3 x^{2} - 18 x - 21 = 0$$
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
$$a = 3$$
$$b = -18$$
$$c = -21$$
, then
D = b^2 - 4 * a * c =
(-18)^2 - 4 * (3) * (-21) = 576
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 7$$
$$x_{2} = -1$$