(4x+5)^0,5-(14-x)^0,5=2 решите уравнение

{\displaystyle {\sqrt {4x+5}}-{\sqrt {14-x}}=2}
{\displaystyle 4x+5-2{\sqrt {4x+5}}·{\sqrt {14-x}}+14-x=4}
{\displaystyle {\sqrt {56x-4^{2}}+70-5x}={\frac {3x+15}{2}}}
{\displaystyle -4x^{2}+51x+70={\frac {9x^{2}+90x+225}{4}}}
{\displaystyle -16x^{2}+204x+280=9x^{2}+90x+225}
{\displaystyle 25x^{2}-114x-55=0}
{\displaystyle D=(-114)^{2}+4·25·55=12996+5500=18496}
{\displaystyle x={\frac {114\pm \{\sqrt {18496}}}{50}}}
{\displaystyle x={\frac {114\pm \136}{50}}}
{\displaystyle \x _{1}\=5}
{\displaystyle \x _{2}\=-{\frac {11}{25}}}  - не удовлетворяет

ответ:  {\displaystyle x=5}