#### Answer

$x=-1,\frac{7}{5}$

#### Work Step by Step

$5x^{2}-2x=7$
Step 1: Move all terms to one side
$5x^{2}-2x-7=0$
Step 2: Split the second term into two terms
$5x^{2}+5x-7x-7=0$
Step 3: Factor out the common term in first two terms and then the last two terms
$5x(x+1)-7(x+1)=0$
Step 4: Factor out the common term x+1
$(x+1)(5x-7)=0$
Step 5: Solve for x
$x=-1,\frac{7}{5}$