Ta có : \(3x^2+5x+14=5\left(x+1\right)\sqrt{4x-1}\)
\(\Leftrightarrow\left(3x^2+5x+14\right)^2=\left[5\left(x+1\right)\sqrt{4x-1}\right]^2\)
\(\Leftrightarrow9x^4+25x^2+196+2\left(3x^2.5x+5x.14+3x^2.14\right)=25.\left(x+1\right)^2\left(4x-1\right)\)
\(\Leftrightarrow9x^4+25x^2+196+2\left(15x^3+70x+42x^2\right)=25\left(x+1\right)^2\left(4x-1\right)\)
\(\Leftrightarrow9x^4+25x^2+196+30x^3+140x+84x^2=25\left(x+1\right)^2\left(4x-1\right)\)
\(\Leftrightarrow9x^4+109x^2+196+30x^3+140x=25\left(x^2+2x+1\right)\left(4x-1\right)\)
\(\Leftrightarrow9x^4+109x^2+196+30x^3+140x=\left(25x^2+50x+25\right)\left(4x-1\right)\)
\(\Leftrightarrow9x^4+109x^2+196+30x^3+140x=\left(25x^2+50x+25\right)\left(4x-1\right)\)
\(\Leftrightarrow9x^4+109x^2+196+30x^3+140x=100x^3+200x^2+100x-25x^2-50x-25\)
\(\Leftrightarrow9x^4+109x^2+196+30x^3+140x=100x^3+175x^2+50x-25\)
Đến đây chuyển vế sang giải nhé mệt quá
