2x^2= 6x -5 solution

Answer:[tex]\large\boxed{\bold{No\ real\ solutio}\\\boxed{\dfrac{3}{2}\pm\dfrac{1}{2}i}[/tex]Step-by-step explanation:[tex]2x^2=6x-5\qquad\text{subtract}\ 2x^2\ \text{from both sides}\\\\0=-2x^2+6x-5\qquad\text{change the signs}\\\\0=2x^2-6x+5\\\\2x^2-6x+5=0\\\\\text{use the quadratic formula:}\\\\ax^2+bx+c=0\\\\if\ b^2-4ac<0,\ then\ the\ equation\ has\ no\ real\ solution\\\\if\ b^2-4ac=0,\ then\ the\ equation\ has\ one\ solution\ x=\dfrac{-b}{2a}\\\\if\ b^2-4ac>0,\ then\ the\ equation\ has\ two\ solutions\ x=\dfrac{-b\pm\sart{b^2-4ac}}{2a}[/tex][tex]2x^2-6x+5=0\\\\a=2,\ b=-6,\ c=5\\\\b^2-4ac=(-6)^2-4(2)(5)=36-40=-4<0\\\\\bold{No\ real\ solution}\\\\\text{If yo want the complex solution, then:}\\\\i=\sqrt{-1}\to\sqrt{-4}=\sqrt{4}\cdot\sqrt{-1}=2i\\\\x=\dfrac{-(-6)\pm2i}{2(2)}=\dfrac{6\pm2i}{4}=\dfrac{3\pm i}{2}=\dfrac{3}{2}\pm\dfrac{1}{2}i[/tex]