If the quadratic equation (a-5) x-4x-1 = 0 with respect to X has real roots, then what is the condition of a?

If the quadratic equation (a-5) x-4x-1 = 0 with respect to X has real roots, then what is the condition of a?

According to the discriminant of the quadratic equation of one variable, it is concluded that:
△=b²-4ac≥0
=(-4)²+4(a-5)≥0
The solution is a ≥ 1
When a ≥ 1, the original equation has real roots

The following equation is transformed into the general form of quadratic equation of one variable: power of 5x-1 = 4x

5x^2-4x-1=0
In the upper right corner of my answer, click [adopt answer]

The solution of X square-5x + 1 = 0

x=〔-(-5)±√(-5)^2-4×1×1〕/2×1
=(5±√21)/2
x1=(5+3√7)/2,x2=(5-3√7)/2

15(4x-8)-5(2x+10)=6(5x-20)

15(4x-8)-5(2x+10)=6(5x-20)
60x-120-10x-50=30x-120
20x=170-120
20x=50
x=2.5