Question

2y ( x-y) +12=5x where x=3

Answer 1

EXPLANATION

Given the expression 2y(x-y) +12=5x , plugging in x=3 into the expression,

2y(3-y) + 12 = 5*3

6y -2y^2 + 12 = 15

Rearranging terms:

`-2y^2+6y+12=15`

Now, we need to apply the quadratic equation:

`\mathrm{For\: a\: quadratic\: equation\: of\: the\: form\: }ax^2+bx+c=0\mathrm{\: the\: solutions\: are\: }`
`x_(1,\: 2)=(-b\pm√(b^2-4ac))/(2a)`
`\mathrm{For\: }\quad a=-2,\: b=6,\: c=-3`
`y_(1,2)=(-6\pm√(6^2-4\left(-2\right)\left(-3\right)))/(2\left(-2\right))`

Multiplying terms:

`y_(1,2)=\frac{-6\pm\sqrt[]{36-24}}{-4}`

Subtracting numbers:

`y_(1,2)=\frac{-6\pm\sqrt[]{12}}{-4}`

Simplifying:

`\mathrm{The\: solutions\: to\: the\: quadratic\: equation\: are\colon}`
`y=(3-√(3))/(2),\: y=(3+√(3))/(2)`