1/4x + 3 = 2x - 5/8
Find least common multiplier of 4x,8 is 8x
Multiply by LCM = 8x
1/4 x * 8 x + 3 * 8 x = 2 x * 8 x - 5/8 * 8 x
Refine:
2 + 24 = 16 x² - 5 x
Subtract 16 x² - 5 x from both sides:
2 + 24 x - ( 16 x² -5 x) = 16 x² - 5 x - (16 x²-5 x)
Refine: - 16 x² - 29 x + 2 = 0
Solving with the quadratic formula :
for a = - 16 , b = 29 and c = 2
x1 = - 29 √ 29² - 4(-16)*2
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2 (-16)
x1 = - √ 969 - 29
---------------------
32
x2 = - 29 - √ 29² -4(-16)*2
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2(-16)
x2 = √ 969 + 29
---------------------
32
The final solutions to the quadratic equation are:
x1 = - √ 969 - 29
-------------------
32
x2 = √ 969 + 29
-------------------
32
hope this helps!