# How do you solve sqrt(2X+3)=sqrt(5X-6)?

Jul 19, 2015

Square both sides and solve the resulting linear equation to find:

$X = 3$

#### Explanation:

First square both sides of the equation to get:

$2 X + 3 = 5 X - 6$

Note that in general squaring both sides of an equation may result in spurious solutions, so we will check later. (Alternatively, we could note at this stage that both sides of the equation are $\ge 0$, so there will be no spurious solution introduced by squaring.)

Next add $6$ to both sides to get:

$2 X + 9 = 5 X$

Subtract $2 X$ from both sides to get:

$9 = 3 X$

Divide both sides by $3$ to get $X = 3$

Now check:

If $X = 3$

then $\sqrt{2 X + 3} = \sqrt{6 + 3} = \sqrt{9} = 3$

and $\sqrt{5 X - 6} = \sqrt{15 - 6} = \sqrt{9} = 3$