Solve for x.
2x² - 5bx + 4cx - 10bc = 0
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Or, just using inspection, or distribution, or grouping,
2x^2 + (4c-5b)x - 10bc = 0
(2x - 5b)(x + 2c) = 0
so, x = 5b/2 or -2c
To solve the quadratic equation for x, you can use the quadratic formula:
x = (-b ± sqrt(b² - 4ac)) / (2a)
In this case, the equation is: 2x² - 5bx + 4cx - 10bc = 0
Comparing this equation with the standard quadratic equation, we can identify:
a = 2
b = -5b
c = 4c - 10bc
Using these values, we can substitute them into the quadratic formula:
x = [ -(-5b) ± sqrt((-5b)² - 4(2)(4c - 10bc)) ] / (2 * 2)
Simplifying further:
x = [5b ± sqrt(25b² - 8(4c - 10bc))] / 4
x = [5b ± sqrt(25b² - 32c + 80bc)] / 4
Therefore, x can be expressed as:
x = (5b + sqrt(25b² - 32c + 80bc)) / 4
x = (5b - sqrt(25b² - 32c + 80bc)) / 4