Answer
$8$.
Work Step by Step
From the question we have
$\Rightarrow \sqrt{5x-4}=x-2$
Square both sides.
$\Rightarrow (\sqrt{5x-4})^2=(x-2)^2$
Use the special formula $(A-B)^2=A^2-2AB+B^2$
We have $A=x$ and $B=2$
$\Rightarrow 5x-4=(x)^2-2(x)( 2)+(2)^2$
Simplify.
$\Rightarrow 5x-4=x^2-4x+4$
Add $-5x+4$ to both sides.
$\Rightarrow 5x-4-5x+4=x^2-4x+4-5x+4$
Add like terms.
$\Rightarrow 0=x^2-9x+8$
Rewrite the middle term $-9x$ as $-8x-1x$.
$\Rightarrow 0=x^2-8x-1x+8$
Group the terms.
$\Rightarrow 0=(x^2-8x)+(-1x+8)$
Factor out each group.
$\Rightarrow 0=x(x-8)-1(x-8)$
Factor out $(x-8)$.
$\Rightarrow 0=(x-8)(x-1)$
Set each factor equal to zero.
$\Rightarrow x-8=0$ or $x-1=0$
Isolate $x$.
$\Rightarrow x=8$ or $x=1$
Check $x=8$.
$\Rightarrow \sqrt{5(8)-4}=8-2$
$\Rightarrow \sqrt{40-4}=6$
$\Rightarrow \sqrt{36}=6$
$\Rightarrow 6=6$ True.
Check $x=1$.
$\Rightarrow \sqrt{5(1)-4}=1-2$
$\Rightarrow \sqrt{5-4}=-1$
$\Rightarrow \sqrt{1}=-1$
$\Rightarrow 1=-1$ false.
