Question 83085
The given quadratic equation is : {{{5(x-2)^2 = 3 }}} 


Let us first expand the given equation on the left hand side. 


{{{ 5(x^2 + 4 - 4x) = 3}}} 



{{{5x^2 + 20 - 20x - 3 = 0 }}} 



{{{5x^2 - 20x + 17 = 0 }}} 


Solving this equation by using the quadratic formula, we get:  



{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 



Substituing for the values, we get: 



{{{ x = (20 +- sqrt(400 - 4(5)(17))/2(5)) }}} 



{{{ x = (20 +- sqrt(400 - 340))/10}}} 


{{{x = (20 +- sqrt(60))/10}}} 



{{{x = (20 +- sqrt(15 * 4))/10}}} 


{{{x = (20 +- 2*sqrt(15))/10}}} 



{{{x = (10+- sqrt(15))/5}}} 



Hence, the values of x. 



Thus, the solution.