Explanation:
SOLUTION
\small\textsf{Let y = 15 and rearrange the terms}Let y = 15 and rearrange the terms
\small\sf{y = 8x - {x}^{2} }y=8x−x
2
\small\sf{15 = 8x - {x}^{2} }15=8x−x
2
\small\sf{15 + ( - 15)= 8x - {x}^{2} + ( - 15)}15+(−15)=8x−x
2
+(−15)
\small\sf{ {x}^{2} - 8x + 15 = 0 }x
2
−8x+15=0
\small\textsf{Solve the quadratic equation and find x}Solve the quadratic equation and find x
\small\sf{ {x}^{2} - 8x + 15 = 0 }x
2
−8x+15=0
\small\sf{ {x}^{2} - 3x - 5x + 15 = 0 }x
2
−3x−5x+15=0
\small\sf{ x(x - 3) - 5(x - 3) = 0 }x(x−3)−5(x−3)=0
\small\sf{ (x - 3)(x - 5 ) = 0 }(x−3)(x−5)=0
\small\sf{ x - 3 = 0 }x−3=0
\small\sf{ x - 3 + 3 = 0 + 3 }x−3+3=0+3
\small\boxed{\green{\sf{x = 3s }}}
x=3s
\small\sf{x - 5 = 0}x−5=0
\small\sf{x - 5 + 5 = 0 + 5}x−5+5=0+5
\small\boxed{\green{\sf{x = 5s }}}
x=5s
