1.25=z^2+z

Solution for 1.25=z^2+z equation:

1.25=z^2+z

We move all terms to the left:

1.25-(z^2+z)=0

We get rid of parentheses

-z^2-z+1.25=0

We add all the numbers together, and all the variables

-1z^2-1z+1.25=0

a = -1; b = -1; c = +1.25;
Δ = b2-4ac
Δ = -12-4·(-1)·1.25
Δ = 6
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{6}}{2*-1}=\frac{1-\sqrt{6}}{-2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{6}}{2*-1}=\frac{1+\sqrt{6}}{-2}
$