How do you solve #4x^2 <(12x-9)#? Precalculus Solving Rational Inequalities Polynomial Inequalities 1 Answer Shwetank Mauria Sep 2, 2016 #4x^2<12x-9# does not have any solution. Explanation: #4x^2<12x-9# #hArr4x^2-12x+9<0# or #(2x)^2-2×2x×3+3^2<0# or #(2x-3)^2<0# i.e. #(2x-3# is negative. But a square number can not be negative. Hence #4x^2<12x-9# does not have any solution. Answer link Related questions What are common mistakes students make when solving polynomial inequalities? How do I solve a polynomial inequality? How do I solve the polynomial inequality #-2(m-3)<5(m+1)-12#? How do I solve the polynomial inequality #-6<=2(x-5)<7#? How do I solve the polynomial inequality #1<2x+3<11#? How do I solve the polynomial inequality #-12<-2(x+1)<=18#? How do you solve the inequality #6x^2-5x>6#? How do you solve #x^2 - 4x - 21<=0# A) [-3, 7] B) (-∞, -3] C) (-∞, -3] [7, ∞) D) [7, ∞)? How do you solve quadratic inequality, graph, and write in interval notation #x^2 - 8x + 15 >0#? How do you solve #-x^2 - x + 6 < 0#? See all questions in Polynomial Inequalities Impact of this question 1552 views around the world You can reuse this answer Creative Commons License