Punem conditia ca Δ (delta) sa fie strict mai mare decat 0
[tex]delta= b^{2} -4ac=a^{2} -4(a-1)=a^{2} -4a+4= (a-2)^{2} \\=> delta >0 => a-2>0 => a>2[/tex]
Verificam daca solutiile sunt distincte
[tex]x_{12} (solutiile)=\frac{-b + sau-\sqrt{delta} }{2a} =\frac{a+ sau-(a-2)}{2} \\=> x_{1} =\frac{a+a-2}{2} =\frac{2a-2}{2} =\frac{2(a-1)}{2} =a-1 (real)\\=> x_{2} =\frac{a-(a-2)}{2} =\frac{a-a+2}{2} =\frac{2}{2} =1 (real)[/tex]
Verificam daca solutiile sunt corecte
[tex]Cazul 1: x_{1} =a-1\\=> (a-1)^{2} -a(a-1)+a-1=0\\=> a^{2} -2a+1-a^{2} +a+a-1=0\\=> 0=0 (adevarat)[/tex]
[tex]Cazul2 : x_{2} =1 \\=> 1^{2} -a*1+a-1=0\\=> 0=0 (adevarat)[/tex]