1. x²+√2x - 4=02. 4(x+1)²-25=03.(5x+ 4,5 )²= 12¼4.4x²+9x=05.(1-7x)(2x+1)-(3-5x)(2x+1)=0.... Question from @minjee

1.
$x^2+\sqrt{2}-4=0$

$delta=b^2-4ac$

$delta=2+16\\ delta=18\\ \sqrt{delta}=\sqrt{18}\\ \sqrt{delta}=3 \sqrt{2}\\ x_{1}=\frac{-b-\sqrt{delta}}{2a}\ \ \ \ \ \ x_{2}=\frac{-b+\sqrt{delta}}{2a}\\$ $x_{1}=\frac{-\sqrt{2}-3\sqrt{2}}{2}\ \ \ \ \ \ x_{2}=\frac{-\sqrt{2}+3\sqrt{2}}{2}\\ x_{1}=\frac{-4\sqrt{2}}{2}\ \ \ \ \ \ x_{2}=\frac{2\sqrt{2}}{2}\\ x_{1}=-2\sqrt{2}\ \ \ \ \ \ x_{2}=\sqrt{2}$

$4(x+1)^2-25=0\\ 4(x^2+2x+1)-25=0\\ 4x^2+8x+4-25=0\\ 4x^2+8x-21=0\\ delta=b^2-4ac\\ delta=64+336\\ delta=400\\ \sqrt{delta}=20\\\ \\ x_{1}=\frac{-8-20}{8}\ \ \ x_{2}=\frac{-8+20}{8}\\ x_{1}=-3\frac{1}{2}\ \ \ x_{2}=1\frac{1}{2}$

$(5x+ 4,5 )^2= 12\frac{1}{4}\\ 25x^2+45x+20\frac{1}{4}=12\frac{1}{4}\\ 25x^2+45x+8=0\\ delta=2025-800\\ delta=1225\\ \sqrt{delta}=35\\ x_{1}=\frac{-45-35}{50}\ \ \ x_{2}=\frac{-45+35}{50}\\ x_{1}=1\frac{3}{5}\ \ \ x_{2}=\frac{1}{5}$