Please help. What is/are the equation(s) needed to solve this problem

A swimming pool is to be built on a lawn that measures 25m by 20m. When the pool is built, the remaining lawn will form a boarder of uniform width around the pool. The remaining area of the lawn is to equal 85% of the area of the swimming pool. How wide is the lawn and what are the dimensions of the swimming pool?

Let the width of the border = x

25*20 - (25 - 2x)(20 - 2x) = 0.85(25 - 2x)(20 - 2x)

25*20 = 1.85(25 - 2x)(20 - 2x)

500 = 1.85(4x^2 - 90x + 500)

500 = 7.4x^2 - 166.5x + 925

0 = 7.4x^2 - 166.5x + 425

a = 7.4
b = -166.5
c = 425

x = [166.5 +/- sqrt(27722.25 - 4*7.4*425)] / 14.8

x = [166.5 +/- sqrt(15142.25)] / 14.8

x approximately 19.56m or 2.94m

19.56 makes for a REALLY wide border and not much pool.

For 2.94m width lawn, pool is (25 - 2x)(20 - 2x)

19.129m x 14.129m pool
=======================================…
For 19.56m width lawn, dimensions become negative. Disregard.


Area of pool is 270.27 sq m

Area of lawn = 500 - 270.27 = 229.73 sq m

total area = 25·20 = 500 m²
width of border = x meters, x < 10 m
pool area = (25 - 2x)(20 - 2x) = 4x² - 90x + 500

pool area = total area /185% = 270.270
4x² - 90x + 500 = 270.270
4x² - 90x + 229.7297 = 0
By the quadratic formula, x ≅ 2.936, 19.564
x ≅ 2.936 meters

length of pool = 25 - 2x ≅ 19.129 m
width of pool = 20 - 2x = 14.129 m