Question 975126
{{{2sqrt(1-x)=3sqrt(2x-1)+1}}}
{{{4(1-x)=9(2x-1)+6sqrt(2x-1)+1}}}
{{{4(1-x)-9(2x-1)-1=6sqrt(2x-1)}}}, notice that the indicated distributive property multiplications have not yet been performed; only still isolating the irrational expression.


LeftSide, {{{4-4x-18x+9}}}
{{{-22x+13}}}
{{{13-22x}}}


Revised equation,
{{{13-22x=6sqrt(2x-1)}}}
Square both sides,
{{{169-2*13*22x+22^2*x^2=36(2x-1)}}}
{{{169-572x+484x^2=72x-36}}}
{{{484x^2-572x+169-72x+36=0}}}
{{{highlight_green(484x^2-644x+205=0)}}}


Use the general solution for a quadratic equation.
Discriminant, {{{644^2-4*484*205=17856=8*2232=8*8*279=8*8*9*31}}}
{{{sqrt(8*8*9*31)=24sqrt(31)}}}
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{{{x=(644+- 24sqrt(31))/(2*484)}}}


{{{x=(644+- 24sqrt(31))/(2*4*121)}}}


{{{highlight(x=(161+- 6sqrt(31))/(242))}}}