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\: }$$x_{1,\: 2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$\mathrm{For\: }\quad a=-2,\: b=6,\: c=-3$$y_{1,2}=\frac{-6\pm\sqrt{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=\frac{3-\sqrt{3}}{2},\: y=\frac{3+\sqrt{3}}{2}$