-x^2+4x+5-(x^2-x+5)=0

Solution for -x^2+4x+5-(x^2-x+5)=0 equation:

-x^2+4x+5-(x^2-x+5)=0

We add all the numbers together, and all the variables

-1x^2+4x-(x^2-x+5)+5=0

We get rid of parentheses

-1x^2-x^2+4x+x-5+5=0

We add all the numbers together, and all the variables

-2x^2+5x=0

a = -2; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-2)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-2}=\frac{0}{-4}
=0
$