0.25x2+x-5=-x-8

Solution for 0.25x2+x-5=-x-8 equation:

0.25x^2+x-5=-x-8

We move all terms to the left:

0.25x^2+x-5-(-x-8)=0

We add all the numbers together, and all the variables

0.25x^2+x-(-1x-8)-5=0

We get rid of parentheses

0.25x^2+x+1x+8-5=0

We add all the numbers together, and all the variables

0.25x^2+2x+3=0

a = 0.25; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·0.25·3
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-1}{2*0.25}=\frac{-3}{0.5}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+1}{2*0.25}=\frac{-1}{0.5}
=-2
$