Помогите решить пожалуйста уравнение: 4^x-(a-1)*2^(x+1)+a^2-4a+3=0

4 ^ x - ( a - 1 ) * 2 ^ ( x + 1 ) + a ^ 2 - 4 * a + 3 = 0 ;
( 2 ^ x ) ^ 2 - ( a - 1 ) * 2 ^ x * 2 + a ^ 2 - 4 * a + 3 = 0 ;
( 2 ^ x ) ^ 2 - 2 * ( a - 1 ) * 2 ^ x + a ^ 2 - 4 * a + 3 = 0 ;
Пусть 2 ^ x = t, тогда:
t ^ 2 - 2 * ( a - 1 ) * t + a ^ 2 - 4 * a + 3 = 0 ;
Дискриминант = ( 2 * ( a - 1 ) ) ^ 2 - 4 * 1 * ( a ^ 2 - 4 * a + 3 ) = 4 * ( a ^ 2 - 2 * a + 1 ) - 4 * ( a ^ 2 - 4 * a + 3 ) = 4 * a ^ 2 - 8 * a + 4 - 4 * a ^ 2 + 16 * a - 12 = 16 * a - 8 * a + 4 - 12 = 8 * a - 8 ;
t1 = ( + 2 * ( a - 1 ) + ( 8 * a - 8 ) ) / ( 2 * 1 ) = ( + 2 * ( a - 1 ) + 2 * 2 * ( a - 1 ) ) / 2 = a - 1 + 2 * ( a - 1 ) = a - 1 + 2 * a - 2 = a * ( 1 + 2 ) - ( 1 + 2 ) = ( 1 + 2 ) * ( a - 1 ) ;
t2 = ( + 2 * ( a - 1 ) - ( 8 * a - 8 ) ) / ( 2 * 1 ) = ( + 2 * ( a - 1 ) - 2 * 2 * ( a - 1 ) ) / 2 = a - 1 - 2 * ( a - 1 ) = a - 1 - 2 * a + 2 = a * ( 1 - 2 ) - ( 1 - 2 ) = ( 1 - 2 ) * ( a - 1 );
Тогда:
1 ) 2 ^ x = ( 1 + 2 ) * ( a - 1 ) ;
x = log2 ( ( 1 + 2 ) * ( a - 1 ) ) ;
2 ) 2 ^ x = ( 1 - 2 ) * ( a - 1 ) ;
x = log2 ( ( 1 - 2 ) * ( a - 1 ) ).