0=-5x-x^2/8-10

Solution for 0=-5x-x^2/8-10 equation:

0=-5x-x^2/8-10

We move all terms to the left:

0-(-5x-x^2/8-10)=0

We add all the numbers together, and all the variables

-(-5x-x^2/8-10)=0

We get rid of parentheses

x^2/8+5x+10=0

We multiply all the terms by the denominator


x^2+5x*8+10*8=0

We add all the numbers together, and all the variables

x^2+5x*8+80=0

Wy multiply elements

x^2+40x+80=0

a = 1; b = 40; c = +80;
Δ = b2-4ac
Δ = 402-4·1·80
Δ = 1280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-16\sqrt{5}}{2*1}=\frac{-40-16\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+16\sqrt{5}}{2*1}=\frac{-40+16\sqrt{5}}{2}
$