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

Solution for -2x+5-(x-1)(x+2)=0 equation:

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

We multiply parentheses ..

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

We get rid of parentheses

-x^2-2x+1x-2x+2+5=0

We add all the numbers together, and all the variables

-1x^2-3x+7=0

a = -1; b = -3; c = +7;
Δ = b2-4ac
Δ = -32-4·(-1)·7
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{37}}{2*-1}=\frac{3-\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{37}}{2*-1}=\frac{3+\sqrt{37}}{-2}
$