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(A) $I.$ For the equation $63x^2 + 172x + 117 = 0$:We need to factorize $63 	imes 117 = 7371$ into two numbers that add up to $172$. These are $91$ a

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if $x > y$

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(A) $I.$ For the equation $63x^2 + 172x + 117 = 0$:We need to factorize $63 	imes 117 = 7371$ into two numbers that add up to $172$. These are $91$ and $81$.$63x^2 + 91x + 81x + 117 = 0$$7x(9x + 13) + 9(9x + 13) = 0$$(7x + 9)(9x + 13) = 0$So,$x = -9/7 \approx -1.28$ and $x = -13/9 \approx -1.44$.$II.$ For the equation $30y^2 + 162y + 216 = 0$:Divide by $6$: $5y^2 + 27y + 36 = 0$.We need to factorize $5 	imes 36 = 180$ into two numbers that add up to $27$. These are $15$ and $12$.$5y^2 + 15y + 12y + 36 = 0$$5y(y + 3) + 12(y + 3) = 0$$(5y + 12)(y + 3) = 0$So,$y = -12/5 = -2.4$ and $y = -3$.Comparing the values:$x$ values are $\approx -1.28, -1.44$.$y$ values are $-2.4, -3$.Since both values of $x$ are greater than both values of $y$,$x > y$.

Solve the given two equations and select the correct option.
$I.$ $63x^2 + 172x + 117 = 0$
$II.$ $30y^2 + 162y + 216 = 0$

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Solve the given two equations and select the correct option.$I.$ $63x^2 + 172x + 117 = 0$$II.$ $30y^2 + 162y + 216 = 0$