what does 2x^2−3x−5=0 in a quadratic equation?

2x²-3x-5=0

2x²-5x+2x-5=0

x(2x-5)+(2x-5)=0

(x+1)(2x-5)=0

x+1=0 , x=-1

2x+5=0 , x=-5/2

${2x}^{2}-3x-5=0$

${2x}^{2}-5x+2x-5=0$

$({2x}^{2}-5x)+(2x-5)=0$

$x\times(2x-5)+1\times(2x-5)=0$

$(x+1)(2x-5)=0$

$x+1=0$  $2x-5=0$

$x+1=0$

$x=-1$

$2x-5=0$

$2x=5$

$x=\frac{5}{2}$

$x=-1$ and $x=\frac{5}{2}$