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2x²+3x<4 solve the inequalities

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Jers15viz
2x²+3x<4
Subtract both sides by 4
2x²+3x-4<0
Use by completing the square
so first divide both sides by 2
x²+3/2(x)-2<0
x²+3/2(x)<2
x²+3/2(x)+9/16<41/16
(x²+3/4)²<41/16
square root both sides
x+3/4<√41/4
x=posineg√41/4-3/4