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Question:

Solve for x: √3x² - 2 + √2x - 2 + √3 = 0

Solution:

We know that for ax² + bx + c = 0, x = −b ± √b² − 4ac / 2a
√3x² - 2 + √2x - 2 + √3 = 0
x = −(−2 + √2) ± √(−2 + √2)² − 4 × √3 × (−2 + √3) / 2√3
= 2 + √2 ± √8 + 24 / 2√3
= 2 + √2 ± √32 / 2√3
= 2 + √2 ± 4√2 / 2√3
= √2 ± 2√2 / √3
x = √2 + 2√2 / √3 = 3√2 / √3
Or
x = √2 - 2√2 / √3 = -√2 / √3