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