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Equation (7-2x)(9-2x)-35=0
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(7-2x)(9-2x)-35=0 equation
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The solution
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(7 - 2*x)*(9 - 2*x) - 35 = 0
$$\left(7 - 2 x\right) \left(9 - 2 x\right) - 35 = 0$$
Detail solution
Expand the expression in the equation
$$\left(7 - 2 x\right) \left(9 - 2 x\right) - 35 = 0$$
We get the quadratic equation
$$4 x^{2} - 32 x + 28 = 0$$
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
$$a = 4$$
$$b = -32$$
$$c = 28$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 7$$
$$x_{2} = 1$$
$$\left(7 - 2 x\right) \left(9 - 2 x\right) - 35 = 0$$
We get the quadratic equation
$$4 x^{2} - 32 x + 28 = 0$$
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
$$a = 4$$
$$b = -32$$
$$c = 28$$
, then
D = b^2 - 4 * a * c =
(-32)^2 - 4 * (4) * (28) = 576
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 7$$
$$x_{2} = 1$$
The graph