Answer:
[tex]\red{ \bold{ 7 {x}^{2} + 180x + 324 = 0}}[/tex]
Step-by-step explanation:
Given is an isosceles right triangle.
Therefore, by Pythagoras theorem:
[tex] {(5x + 18)}^{2} = {( - 3x)}^{2} + {( - 3x)}^{2} \\ \\ \implies \: {(5x)}^{2} + 2(5x)(18) + {(18)}^{2} = 9 {x}^{2} + 9 {x}^{2} \\ \\ \implies \: 25 {x}^{2} + 180x + 324 = 18 {x}^{2} \\ \\ \implies \: 25 {x}^{2} - 18 {x}^{2} + 180x + 324 = 0 \\ \\ \implies \: \ \red{ \bold{ 7 {x}^{2} + 180x + 324 = 0}}\\ \\ [/tex]
