6.25=x+x^2

Solution for 6.25=x+x^2 equation:

6.25=x+x^2

We move all terms to the left:

6.25-(x+x^2)=0

We get rid of parentheses

-x^2-x+6.25=0

We add all the numbers together, and all the variables

-1x^2-1x+6.25=0

a = -1; b = -1; c = +6.25;
Δ = b2-4ac
Δ = -12-4·(-1)·6.25
Δ = 26
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{-(-1)-\sqrt{26}}{2*-1}=\frac{1-\sqrt{26}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{26}}{2*-1}=\frac{1+\sqrt{26}}{-2}
$