how do you solve this can you do this with the steps do I an understand them,please.

square root start 5x-4 square root end = 7- square root start 13-x square root end

thanks for your time and help

To solve the equation:

√(5x - 4) = 7 - √(13 - x)

Step 1: Isolate one square root term on one side of the equation.
Start by moving the term containing the square root on the right side of the equation to the left side:
√(5x - 4) + √(13 - x) = 7

Step 2: Square both sides of the equation to eliminate the square roots.
(√(5x - 4) + √(13 - x))^2 = 7^2

Step 3: Expand the squared expression on the left side.
(√(5x - 4))^2 + 2(√(5x - 4))(√(13 - x)) + (√(13 - x))^2 = 49

Step 4: Simplify and get rid of the square roots.
5x - 4 + 2√((5x - 4)(13 - x)) + 13 - x = 49

Step 5: Combine like terms.
4x + 9 + 2√((5x - 4)(13 - x)) = 49

Step 6: Move all terms involving the square root to the right side.
2√((5x - 4)(13 - x)) = 49 - 9 - 4x

Step 7: Simplify.
2√((5x - 4)(13 - x)) = 40 - 4x

Step 8: Square both sides again to eliminate the remaining square root.
[2√((5x - 4)(13 - x))]^2 = (40 - 4x)^2

Step 9: Expand the squared expression on the left side.
4((5x - 4)(13 - x)) = (40 - 4x)^2

Step 10: Simplify.
4(65x - 60x + 56) = (40 - 4x)(40 - 4x)

Step 11: Expand and simplify.
260x - 240x + 224 = 1600 - 320x + 16x^2

Step 12: Rearrange the equation to a quadratic form.
16x^2 - 388x + 1376 = 0

Now you have a quadratic equation that can be solved using the quadratic formula or factoring techniques.