Answer:
The solution of the equation is [tex]x=1[/tex]
Step-by-step explanation:
we have
[tex]5x=\sqrt{10+15x}[/tex]
squared both sides
[tex]25x^{2}=10+15x[/tex]
[tex]25x^{2}-15x-10=0[/tex]
Using a graphing tool------> to resolve the quadratic equation
The solution of the quadratic equation are
[tex]x=-0.4,x=1[/tex]
see the attached figure
Substitute in the original equation to verify the solution
For [tex]x=-0.4[/tex]
[tex]5(-0.4)=\sqrt{10+15(-0.4)}[/tex]
[tex]-2=\sqrt{4}[/tex]
[tex]-2=2[/tex] -----> is not true
For [tex]x=1[/tex]
[tex]5(1)=\sqrt{10+15(1)}[/tex]
[tex]5=\sqrt{25}[/tex]
[tex]5=5[/tex] -----> is true
therefore
The solution of the equation is [tex]x=1[/tex]
