Can someone explain to me why this is right?

Hello!

This is right because the goal of solving a quadratic equation is to isolate the variable and then solve it. First you multiply - 8/3 to both sides to isolate s and the you solve the equation by multiplying - 8/3 to - 6

actual yield of ethanol = 305.0g

molar mass of sucrose = 342g

molar mass of ethanol  =46g

mass of sucrose = 665g

mole of sucrose = mass / molar mass = 665/342

mole of sucrose =1.9 mole

sucrose :  C2H5OH

       1      :  4

     1.9     : 1.9x4 =7.6 mole of C2H5OH are formed

mass (therotical yield ) of C2H5OH= mole x mass

mass (therotical yield ) of C2H5OH= 7.6 x 46 = 349.6g

percent yields of ethanol =  actual /therotical x100

=305/349.6x100 = 87.24 %