Question

2x^2= 6x -5 solution

Answer 1

Explanation:

`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=(-b)/(2a)\\\\if\ b^2-4ac>0,\ then\ the\ equation\ has\ two\ solutions\ x=\frac{-b\pm\sart{b^2-4ac}}{2a}`

`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=√(-1)\to√(-4)=√(4)\cdot√(-1)=2i\\\\x=(-(-6)\pm2i)/(2(2))=(6\pm2i)/(4)=(3\pm i)/(2)=(3)/(2)\pm(1)/(2)i`