The given equation is,
[tex]-5x^2^{}=5x-2[/tex]
Rearranging the equation, we have,
[tex]5x^2+5x-2=0[/tex]
Here, a = 5, b = 5, c = -2. Therefore, the discriminant can be calculated as,
[tex]b^2-4ac=5^2+4\times5\times2=65[/tex]
The discriminant is 65, and hence it has two distinct real number solutions.
Now, solving for x, we get,
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{-5\pm\sqrt[]{65}}{2\times5}=\frac{-1+\sqrt[]{65}}{2},\text{ }\frac{\text{-1-}\sqrt[]{65}}{2}[/tex]
