`sqrt(2x+3) + sqrt(10-2x) = 5`
`tosqrt(2x+3) = 5- sqrt(10-2x)`
`to(sqrt(2x+3))^2 =( 5- sqrt(10-2x))^2`
`to2x+3 =25-10 sqrt(10-2x)+(10-2x)`
`to2x+3 =25-10 sqrt(10-2x)+10-2x`
`to2x+3 =35-10 sqrt(10-2x)-2x`
`to4x-32 =10 sqrt(10-2x)`
`to(4x-32 )^2=(10 sqrt(10-2x))^2`
`to16x^2-256x+1024=10 0(10-2x)`
`to16x^2-256x+1024=10 00-200x`
`to16x^2-56x+24=0`
`to8(2x^2-7x+3)=0`
`to2x^2-7x+3=0`
`to2x^2-6x-x+3=0`
`to2x(x-3)-(x-3)=0`
`to(x-3)(2x-1)=0`
\(\to\left[ \begin{array}{l}x=3\\x=\dfrac12\end{array} \right.\)
