1.25x^2=1-x

Solution for 1.25x^2=1-x equation:

1.25x^2=1-x

We move all terms to the left:

1.25x^2-(1-x)=0

We add all the numbers together, and all the variables

1.25x^2-(-1x+1)=0

We get rid of parentheses

1.25x^2+1x-1=0

We add all the numbers together, and all the variables

1.25x^2+x-1=0

a = 1.25; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·1.25·(-1)
Δ = 6
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{6}}{2*1.25}=\frac{-1-\sqrt{6}}{2.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{6}}{2*1.25}=\frac{-1+\sqrt{6}}{2.5}
$